Quantum states from classical states?

[himog]

Is there a legitimate way to define a quantum state as some kind of
superposition of classical states?

[Hontas F. Farmer III]

himog wrote:

> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

No. Here is why.

Classical measurements are averages of quantum states.
for example consider the thermodynamic description of gas
in a balloon. Suppose you want to measure the energy of the gas
E. All you would do is take a thermometer
determine the temperature T then do a little math to get E=3/2 K_B T (is
that right?)

However if we look closer at what has happened we would see that each
particle in the gas has a different energy. When the thermometer
touches the balloon it only measures the energies of the particles
that struck it and reports a time-averaged result for T. Hence the
calculated energy would be a time-averaged result.

In general the macroscopic classical state will always be an average
of microscopic quantum states.

More mathematical terms
\widetilde{E} = Energy operator
|\psi> = State vector
<\psi| = State oneform (or dual vector,or co variant vector in some places).

<E>=<\psi|\widetilde{E}|\psi>
=\int\psi*\widetilde{E}\psi d\mu

[Hontas F. Farmer III]

himog wrote:

> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

No. Here is why.

Classical measurements are averages of quantum states.
for example consider the thermodynamic description of gas
in a balloon. Suppose you want to measure the energy of the gas
E. All you would do is take a thermometer
determine the temperature T then do a little math to get E=3/2 K_B T (is
that right?)

However if we look closer at what has happened we would see that each
particle in the gas has a different energy. When the thermometer
touches the balloon it only measures the energies of the particles
that struck it and reports a time-averaged result for T. Hence the
calculated energy would be a time-averaged result.

In general the macroscopic classical state will always be an average
of microscopic quantum states.

More mathematical terms
\widetilde{E} = Energy operator
|\psi> = State vector
<\psi| = State oneform (or dual vector,or co variant vector in some places).

<E>=<\psi|\widetilde{E}|\psi>
=\int\psi*\widetilde{E}\psi d\mu

[Hontas F. Farmer III]

himog wrote:

> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

No. Here is why.

Classical measurements are averages of quantum states.
for example consider the thermodynamic description of gas
in a balloon. Suppose you want to measure the energy of the gas
E. All you would do is take a thermometer
determine the temperature T then do a little math to get E=3/2 K_B T (is
that right?)

However if we look closer at what has happened we would see that each
particle in the gas has a different energy. When the thermometer
touches the balloon it only measures the energies of the particles
that struck it and reports a time-averaged result for T. Hence the
calculated energy would be a time-averaged result.

In general the macroscopic classical state will always be an average
of microscopic quantum states.

More mathematical terms
\widetilde{E} = Energy operator
|\psi> = State vector
<\psi| = State oneform (or dual vector,or co variant vector in some places).

<E>=<\psi|\widetilde{E}|\psi>
=\int\psi*\widetilde{E}\psi d\mu

[Hontas F. Farmer III]

himog wrote:

> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

No. Here is why.

Classical measurements are averages of quantum states.
for example consider the thermodynamic description of gas
in a balloon. Suppose you want to measure the energy of the gas
E. All you would do is take a thermometer
determine the temperature T then do a little math to get E=3/2 K_B T (is
that right?)

However if we look closer at what has happened we would see that each
particle in the gas has a different energy. When the thermometer
touches the balloon it only measures the energies of the particles
that struck it and reports a time-averaged result for T. Hence the
calculated energy would be a time-averaged result.

In general the macroscopic classical state will always be an average
of microscopic quantum states.

More mathematical terms
\widetilde{E} = Energy operator
|\psi> = State vector
<\psi| = State oneform (or dual vector,or co variant vector in some places).

<E>=<\psi|\widetilde{E}|\psi>
=\int\psi*\widetilde{E}\psi d\mu

[Hontas F. Farmer III]

himog wrote:

> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

No. Here is why.

Classical measurements are averages of quantum states.
for example consider the thermodynamic description of gas
in a balloon. Suppose you want to measure the energy of the gas
E. All you would do is take a thermometer
determine the temperature T then do a little math to get E=3/2 K_B T (is
that right?)

However if we look closer at what has happened we would see that each
particle in the gas has a different energy. When the thermometer
touches the balloon it only measures the energies of the particles
that struck it and reports a time-averaged result for T. Hence the
calculated energy would be a time-averaged result.

In general the macroscopic classical state will always be an average
of microscopic quantum states.

More mathematical terms
\widetilde{E} = Energy operator
|\psi> = State vector
<\psi| = State oneform (or dual vector,or co variant vector in some places).

<E>=<\psi|\widetilde{E}|\psi>
=\int\psi*\widetilde{E}\psi d\mu

[Hontas F. Farmer III]

himog wrote:

> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

No. Here is why.

Classical measurements are averages of quantum states.
for example consider the thermodynamic description of gas
in a balloon. Suppose you want to measure the energy of the gas
E. All you would do is take a thermometer
determine the temperature T then do a little math to get E=3/2 K_B T (is
that right?)

However if we look closer at what has happened we would see that each
particle in the gas has a different energy. When the thermometer
touches the balloon it only measures the energies of the particles
that struck it and reports a time-averaged result for T. Hence the
calculated energy would be a time-averaged result.

In general the macroscopic classical state will always be an average
of microscopic quantum states.

More mathematical terms
\widetilde{E} = Energy operator
|\psi> = State vector
<\psi| = State oneform (or dual vector,or co variant vector in some places).

<E>=<\psi|\widetilde{E}|\psi>
=\int\psi*\widetilde{E}\psi d\mu

[Hontas F. Farmer III]

himog wrote:

> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

No. Here is why.

Classical measurements are averages of quantum states.
for example consider the thermodynamic description of gas
in a balloon. Suppose you want to measure the energy of the gas
E. All you would do is take a thermometer
determine the temperature T then do a little math to get E=3/2 K_B T (is
that right?)

However if we look closer at what has happened we would see that each
particle in the gas has a different energy. When the thermometer
touches the balloon it only measures the energies of the particles
that struck it and reports a time-averaged result for T. Hence the
calculated energy would be a time-averaged result.

In general the macroscopic classical state will always be an average
of microscopic quantum states.

More mathematical terms
\widetilde{E} = Energy operator
|\psi> = State vector
<\psi| = State oneform (or dual vector,or co variant vector in some places).

<E>=<\psi|\widetilde{E}|\psi>
=\int\psi*\widetilde{E}\psi d\mu

[Hontas F. Farmer III]

himog wrote:

> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

No. Here is why.

Classical measurements are averages of quantum states.
for example consider the thermodynamic description of gas
in a balloon. Suppose you want to measure the energy of the gas
E. All you would do is take a thermometer
determine the temperature T then do a little math to get E=3/2 K_B T (is
that right?)

However if we look closer at what has happened we would see that each
particle in the gas has a different energy. When the thermometer
touches the balloon it only measures the energies of the particles
that struck it and reports a time-averaged result for T. Hence the
calculated energy would be a time-averaged result.

In general the macroscopic classical state will always be an average
of microscopic quantum states.

More mathematical terms
\widetilde{E} = Energy operator
|\psi> = State vector
<\psi| = State oneform (or dual vector,or co variant vector in some places).

<E>=<\psi|\widetilde{E}|\psi>
=\int\psi*\widetilde{E}\psi d\mu

[Hontas F. Farmer III]

himog wrote:

> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

No. Here is why.

Classical measurements are averages of quantum states.
for example consider the thermodynamic description of gas
in a balloon. Suppose you want to measure the energy of the gas
E. All you would do is take a thermometer
determine the temperature T then do a little math to get E=3/2 K_B T (is
that right?)

However if we look closer at what has happened we would see that each
particle in the gas has a different energy. When the thermometer
touches the balloon it only measures the energies of the particles
that struck it and reports a time-averaged result for T. Hence the
calculated energy would be a time-averaged result.

In general the macroscopic classical state will always be an average
of microscopic quantum states.

More mathematical terms
\widetilde{E} = Energy operator
|\psi> = State vector
<\psi| = State oneform (or dual vector,or co variant vector in some places).

<E>=<\psi|\widetilde{E}|\psi>
=\int\psi*\widetilde{E}\psi d\mu

[Igor]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

There might be if you could find a way to express a so-called classical
state in a way that would be completely compatible with the notion of a
quantum state. A classical state has full determinism in the evolution
of congugate pairs such as momentum and position as well as energy and
time. A quantum system, on the other hand, lacks such determinism.
There is a deterministic element to the quantum system, however. This
is the wave function, although it seems to be unobservable.

In quantum systems, due to the Heisenberg uncertainty principle,
dynamic conjugate pairs are represented by noncommuting operators on
the Hilbert space of the wave function, so some knowledge of the
classical variables will always be missing in quantum systems. For
that reason alone, the two are not compatible. Quantum appears to
approach classical only in the limit that Planck's constant goes to
zero.

[Igor]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

There might be if you could find a way to express a so-called classical
state in a way that would be completely compatible with the notion of a
quantum state. A classical state has full determinism in the evolution
of congugate pairs such as momentum and position as well as energy and
time. A quantum system, on the other hand, lacks such determinism.
There is a deterministic element to the quantum system, however. This
is the wave function, although it seems to be unobservable.

In quantum systems, due to the Heisenberg uncertainty principle,
dynamic conjugate pairs are represented by noncommuting operators on
the Hilbert space of the wave function, so some knowledge of the
classical variables will always be missing in quantum systems. For
that reason alone, the two are not compatible. Quantum appears to
approach classical only in the limit that Planck's constant goes to
zero.

[Igor]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

There might be if you could find a way to express a so-called classical
state in a way that would be completely compatible with the notion of a
quantum state. A classical state has full determinism in the evolution
of congugate pairs such as momentum and position as well as energy and
time. A quantum system, on the other hand, lacks such determinism.
There is a deterministic element to the quantum system, however. This
is the wave function, although it seems to be unobservable.

In quantum systems, due to the Heisenberg uncertainty principle,
dynamic conjugate pairs are represented by noncommuting operators on
the Hilbert space of the wave function, so some knowledge of the
classical variables will always be missing in quantum systems. For
that reason alone, the two are not compatible. Quantum appears to
approach classical only in the limit that Planck's constant goes to
zero.

[Igor]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

There might be if you could find a way to express a so-called classical
state in a way that would be completely compatible with the notion of a
quantum state. A classical state has full determinism in the evolution
of congugate pairs such as momentum and position as well as energy and
time. A quantum system, on the other hand, lacks such determinism.
There is a deterministic element to the quantum system, however. This
is the wave function, although it seems to be unobservable.

In quantum systems, due to the Heisenberg uncertainty principle,
dynamic conjugate pairs are represented by noncommuting operators on
the Hilbert space of the wave function, so some knowledge of the
classical variables will always be missing in quantum systems. For
that reason alone, the two are not compatible. Quantum appears to
approach classical only in the limit that Planck's constant goes to
zero.

[Igor]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

There might be if you could find a way to express a so-called classical
state in a way that would be completely compatible with the notion of a
quantum state. A classical state has full determinism in the evolution
of congugate pairs such as momentum and position as well as energy and
time. A quantum system, on the other hand, lacks such determinism.
There is a deterministic element to the quantum system, however. This
is the wave function, although it seems to be unobservable.

In quantum systems, due to the Heisenberg uncertainty principle,
dynamic conjugate pairs are represented by noncommuting operators on
the Hilbert space of the wave function, so some knowledge of the
classical variables will always be missing in quantum systems. For
that reason alone, the two are not compatible. Quantum appears to
approach classical only in the limit that Planck's constant goes to
zero.

[Igor]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

There might be if you could find a way to express a so-called classical
state in a way that would be completely compatible with the notion of a
quantum state. A classical state has full determinism in the evolution
of congugate pairs such as momentum and position as well as energy and
time. A quantum system, on the other hand, lacks such determinism.
There is a deterministic element to the quantum system, however. This
is the wave function, although it seems to be unobservable.

In quantum systems, due to the Heisenberg uncertainty principle,
dynamic conjugate pairs are represented by noncommuting operators on
the Hilbert space of the wave function, so some knowledge of the
classical variables will always be missing in quantum systems. For
that reason alone, the two are not compatible. Quantum appears to
approach classical only in the limit that Planck's constant goes to
zero.

[Igor]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

There might be if you could find a way to express a so-called classical
state in a way that would be completely compatible with the notion of a
quantum state. A classical state has full determinism in the evolution
of congugate pairs such as momentum and position as well as energy and
time. A quantum system, on the other hand, lacks such determinism.
There is a deterministic element to the quantum system, however. This
is the wave function, although it seems to be unobservable.

In quantum systems, due to the Heisenberg uncertainty principle,
dynamic conjugate pairs are represented by noncommuting operators on
the Hilbert space of the wave function, so some knowledge of the
classical variables will always be missing in quantum systems. For
that reason alone, the two are not compatible. Quantum appears to
approach classical only in the limit that Planck's constant goes to
zero.

[Igor]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

There might be if you could find a way to express a so-called classical
state in a way that would be completely compatible with the notion of a
quantum state. A classical state has full determinism in the evolution
of congugate pairs such as momentum and position as well as energy and
time. A quantum system, on the other hand, lacks such determinism.
There is a deterministic element to the quantum system, however. This
is the wave function, although it seems to be unobservable.

In quantum systems, due to the Heisenberg uncertainty principle,
dynamic conjugate pairs are represented by noncommuting operators on
the Hilbert space of the wave function, so some knowledge of the
classical variables will always be missing in quantum systems. For
that reason alone, the two are not compatible. Quantum appears to
approach classical only in the limit that Planck's constant goes to
zero.

[Igor]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

There might be if you could find a way to express a so-called classical
state in a way that would be completely compatible with the notion of a
quantum state. A classical state has full determinism in the evolution
of congugate pairs such as momentum and position as well as energy and
time. A quantum system, on the other hand, lacks such determinism.
There is a deterministic element to the quantum system, however. This
is the wave function, although it seems to be unobservable.

In quantum systems, due to the Heisenberg uncertainty principle,
dynamic conjugate pairs are represented by noncommuting operators on
the Hilbert space of the wave function, so some knowledge of the
classical variables will always be missing in quantum systems. For
that reason alone, the two are not compatible. Quantum appears to
approach classical only in the limit that Planck's constant goes to
zero.

[vonnyn@hotmail.com]

Your idea rests on the hope (a popular one, by the way, often employing
'superselection rules') that some quantum states are classical (or
perhaps 'nearly' so), however this is simply not the case. Some states,
such as squeezed states, may look classical in some regards, but only
by ignoring things you're not interested in. *Every* quantum state is
itself a linear combination of other states (or a mixture of such
combinations), and that gives rise to the possibility of interference
effects - precisely what you *don't* want if you want to call it a
classical state.

To achieve your goal in a *legitimate* way is to resolve the
measurement problem ligitimately, which to date nobody has achieved.

[vonnyn@hotmail.com]

Your idea rests on the hope (a popular one, by the way, often employing
'superselection rules') that some quantum states are classical (or
perhaps 'nearly' so), however this is simply not the case. Some states,
such as squeezed states, may look classical in some regards, but only
by ignoring things you're not interested in. *Every* quantum state is
itself a linear combination of other states (or a mixture of such
combinations), and that gives rise to the possibility of interference
effects - precisely what you *don't* want if you want to call it a
classical state.

To achieve your goal in a *legitimate* way is to resolve the
measurement problem ligitimately, which to date nobody has achieved.

[vonnyn@hotmail.com]

Your idea rests on the hope (a popular one, by the way, often employing
'superselection rules') that some quantum states are classical (or
perhaps 'nearly' so), however this is simply not the case. Some states,
such as squeezed states, may look classical in some regards, but only
by ignoring things you're not interested in. *Every* quantum state is
itself a linear combination of other states (or a mixture of such
combinations), and that gives rise to the possibility of interference
effects - precisely what you *don't* want if you want to call it a
classical state.

To achieve your goal in a *legitimate* way is to resolve the
measurement problem ligitimately, which to date nobody has achieved.

[vonnyn@hotmail.com]

Your idea rests on the hope (a popular one, by the way, often employing
'superselection rules') that some quantum states are classical (or
perhaps 'nearly' so), however this is simply not the case. Some states,
such as squeezed states, may look classical in some regards, but only
by ignoring things you're not interested in. *Every* quantum state is
itself a linear combination of other states (or a mixture of such
combinations), and that gives rise to the possibility of interference
effects - precisely what you *don't* want if you want to call it a
classical state.

To achieve your goal in a *legitimate* way is to resolve the
measurement problem ligitimately, which to date nobody has achieved.

[vonnyn@hotmail.com]

Your idea rests on the hope (a popular one, by the way, often employing
'superselection rules') that some quantum states are classical (or
perhaps 'nearly' so), however this is simply not the case. Some states,
such as squeezed states, may look classical in some regards, but only
by ignoring things you're not interested in. *Every* quantum state is
itself a linear combination of other states (or a mixture of such
combinations), and that gives rise to the possibility of interference
effects - precisely what you *don't* want if you want to call it a
classical state.

To achieve your goal in a *legitimate* way is to resolve the
measurement problem ligitimately, which to date nobody has achieved.

[vonnyn@hotmail.com]

Your idea rests on the hope (a popular one, by the way, often employing
'superselection rules') that some quantum states are classical (or
perhaps 'nearly' so), however this is simply not the case. Some states,
such as squeezed states, may look classical in some regards, but only
by ignoring things you're not interested in. *Every* quantum state is
itself a linear combination of other states (or a mixture of such
combinations), and that gives rise to the possibility of interference
effects - precisely what you *don't* want if you want to call it a
classical state.

To achieve your goal in a *legitimate* way is to resolve the
measurement problem ligitimately, which to date nobody has achieved.

[vonnyn@hotmail.com]

Your idea rests on the hope (a popular one, by the way, often employing
'superselection rules') that some quantum states are classical (or
perhaps 'nearly' so), however this is simply not the case. Some states,
such as squeezed states, may look classical in some regards, but only
by ignoring things you're not interested in. *Every* quantum state is
itself a linear combination of other states (or a mixture of such
combinations), and that gives rise to the possibility of interference
effects - precisely what you *don't* want if you want to call it a
classical state.

To achieve your goal in a *legitimate* way is to resolve the
measurement problem ligitimately, which to date nobody has achieved.

[vonnyn@hotmail.com]

Your idea rests on the hope (a popular one, by the way, often employing
'superselection rules') that some quantum states are classical (or
perhaps 'nearly' so), however this is simply not the case. Some states,
such as squeezed states, may look classical in some regards, but only
by ignoring things you're not interested in. *Every* quantum state is
itself a linear combination of other states (or a mixture of such
combinations), and that gives rise to the possibility of interference
effects - precisely what you *don't* want if you want to call it a
classical state.

To achieve your goal in a *legitimate* way is to resolve the
measurement problem ligitimately, which to date nobody has achieved.

[vonnyn@hotmail.com]

Your idea rests on the hope (a popular one, by the way, often employing
'superselection rules') that some quantum states are classical (or
perhaps 'nearly' so), however this is simply not the case. Some states,
such as squeezed states, may look classical in some regards, but only
by ignoring things you're not interested in. *Every* quantum state is
itself a linear combination of other states (or a mixture of such
combinations), and that gives rise to the possibility of interference
effects - precisely what you *don't* want if you want to call it a
classical state.

To achieve your goal in a *legitimate* way is to resolve the
measurement problem ligitimately, which to date nobody has achieved.

[markwh04@yahoo.com]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

The quantum equivalent of a classical state is a coherent state; the
process of arriving at a quantum theory which has the given classical
state space as its classical limit is known more generally as Berezin
quantization.

[markwh04@yahoo.com]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

The quantum equivalent of a classical state is a coherent state; the
process of arriving at a quantum theory which has the given classical
state space as its classical limit is known more generally as Berezin
quantization.

[markwh04@yahoo.com]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

The quantum equivalent of a classical state is a coherent state; the
process of arriving at a quantum theory which has the given classical
state space as its classical limit is known more generally as Berezin
quantization.

[markwh04@yahoo.com]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

The quantum equivalent of a classical state is a coherent state; the
process of arriving at a quantum theory which has the given classical
state space as its classical limit is known more generally as Berezin
quantization.

[markwh04@yahoo.com]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

The quantum equivalent of a classical state is a coherent state; the
process of arriving at a quantum theory which has the given classical
state space as its classical limit is known more generally as Berezin
quantization.

[markwh04@yahoo.com]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

The quantum equivalent of a classical state is a coherent state; the
process of arriving at a quantum theory which has the given classical
state space as its classical limit is known more generally as Berezin
quantization.

[markwh04@yahoo.com]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

The quantum equivalent of a classical state is a coherent state; the
process of arriving at a quantum theory which has the given classical
state space as its classical limit is known more generally as Berezin
quantization.

[markwh04@yahoo.com]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

The quantum equivalent of a classical state is a coherent state; the
process of arriving at a quantum theory which has the given classical
state space as its classical limit is known more generally as Berezin
quantization.

[markwh04@yahoo.com]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

The quantum equivalent of a classical state is a coherent state; the
process of arriving at a quantum theory which has the given classical
state space as its classical limit is known more generally as Berezin
quantization.

[p.kinsler@imperial.ac.uk]

himog <himog@email.com> wrote:
> Is there a legitimate way to define a quantum state as some
> kind of superposition of classical states?

You might find it interesting to have a look at the
Wigner distribution.

--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/

[p.kinsler@imperial.ac.uk]

himog <himog@email.com> wrote:
> Is there a legitimate way to define a quantum state as some
> kind of superposition of classical states?

You might find it interesting to have a look at the
Wigner distribution.

--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/

[p.kinsler@imperial.ac.uk]

himog <himog@email.com> wrote:
> Is there a legitimate way to define a quantum state as some
> kind of superposition of classical states?

You might find it interesting to have a look at the
Wigner distribution.

--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/

[p.kinsler@imperial.ac.uk]

himog <himog@email.com> wrote:
> Is there a legitimate way to define a quantum state as some
> kind of superposition of classical states?

You might find it interesting to have a look at the
Wigner distribution.

--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/

[p.kinsler@imperial.ac.uk]

himog <himog@email.com> wrote:
> Is there a legitimate way to define a quantum state as some
> kind of superposition of classical states?

You might find it interesting to have a look at the
Wigner distribution.

--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/

[p.kinsler@imperial.ac.uk]

himog <himog@email.com> wrote:
> Is there a legitimate way to define a quantum state as some
> kind of superposition of classical states?

You might find it interesting to have a look at the
Wigner distribution.

--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/

[p.kinsler@imperial.ac.uk]

himog <himog@email.com> wrote:
> Is there a legitimate way to define a quantum state as some
> kind of superposition of classical states?

You might find it interesting to have a look at the
Wigner distribution.

--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/

[p.kinsler@imperial.ac.uk]

himog <himog@email.com> wrote:
> Is there a legitimate way to define a quantum state as some
> kind of superposition of classical states?

You might find it interesting to have a look at the
Wigner distribution.

--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/

[p.kinsler@imperial.ac.uk]

himog <himog@email.com> wrote:
> Is there a legitimate way to define a quantum state as some
> kind of superposition of classical states?

You might find it interesting to have a look at the
Wigner distribution.

--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/

[Arnold Neumaier]

markwh04@yahoo.com wrote:

> himog wrote:
>
>>Is there a legitimate way to define a quantum state as some kind of
>>superposition of classical states?
>
> The quantum equivalent of a classical state is a coherent state; the
> process of arriving at a quantum theory which has the given classical
> state space as its classical limit is known more generally as Berezin
> quantization.

And every quantum state can be written as a superposition of coherent
states, though not in a unique way. Thus the view of quantums states as
superposition of classical (i.e., coherent) states is fully valid.

Of course, under a sufficiemtly nontrivial quantum dynamics,
a coherent state does not remain coherent as time develops;
this explains the departure from classicality in quantum mechanics.

In particular, typical nonlocal entanglement phenomena can be
viewed neatly in terms of superpositions of coherent states
which are spatially well separated.

Arnold Neumaier

[Arnold Neumaier]

markwh04@yahoo.com wrote:

> himog wrote:
>
>>Is there a legitimate way to define a quantum state as some kind of
>>superposition of classical states?
>
> The quantum equivalent of a classical state is a coherent state; the
> process of arriving at a quantum theory which has the given classical
> state space as its classical limit is known more generally as Berezin
> quantization.

And every quantum state can be written as a superposition of coherent
states, though not in a unique way. Thus the view of quantums states as
superposition of classical (i.e., coherent) states is fully valid.

Of course, under a sufficiemtly nontrivial quantum dynamics,
a coherent state does not remain coherent as time develops;
this explains the departure from classicality in quantum mechanics.

In particular, typical nonlocal entanglement phenomena can be
viewed neatly in terms of superpositions of coherent states
which are spatially well separated.

Arnold Neumaier

[Arnold Neumaier]

markwh04@yahoo.com wrote:

> himog wrote:
>
>>Is there a legitimate way to define a quantum state as some kind of
>>superposition of classical states?
>
> The quantum equivalent of a classical state is a coherent state; the
> process of arriving at a quantum theory which has the given classical
> state space as its classical limit is known more generally as Berezin
> quantization.

And every quantum state can be written as a superposition of coherent
states, though not in a unique way. Thus the view of quantums states as
superposition of classical (i.e., coherent) states is fully valid.

Of course, under a sufficiemtly nontrivial quantum dynamics,
a coherent state does not remain coherent as time develops;
this explains the departure from classicality in quantum mechanics.

In particular, typical nonlocal entanglement phenomena can be
viewed neatly in terms of superpositions of coherent states
which are spatially well separated.

Arnold Neumaier

[Arnold Neumaier]

markwh04@yahoo.com wrote:

> himog wrote:
>
>>Is there a legitimate way to define a quantum state as some kind of
>>superposition of classical states?
>
> The quantum equivalent of a classical state is a coherent state; the
> process of arriving at a quantum theory which has the given classical
> state space as its classical limit is known more generally as Berezin
> quantization.

And every quantum state can be written as a superposition of coherent
states, though not in a unique way. Thus the view of quantums states as
superposition of classical (i.e., coherent) states is fully valid.

Of course, under a sufficiemtly nontrivial quantum dynamics,
a coherent state does not remain coherent as time develops;
this explains the departure from classicality in quantum mechanics.

In particular, typical nonlocal entanglement phenomena can be
viewed neatly in terms of superpositions of coherent states
which are spatially well separated.

Arnold Neumaier

[Arnold Neumaier]

markwh04@yahoo.com wrote:

> himog wrote:
>
>>Is there a legitimate way to define a quantum state as some kind of
>>superposition of classical states?
>
> The quantum equivalent of a classical state is a coherent state; the
> process of arriving at a quantum theory which has the given classical
> state space as its classical limit is known more generally as Berezin
> quantization.

And every quantum state can be written as a superposition of coherent
states, though not in a unique way. Thus the view of quantums states as
superposition of classical (i.e., coherent) states is fully valid.

Of course, under a sufficiemtly nontrivial quantum dynamics,
a coherent state does not remain coherent as time develops;
this explains the departure from classicality in quantum mechanics.

In particular, typical nonlocal entanglement phenomena can be
viewed neatly in terms of superpositions of coherent states
which are spatially well separated.

Arnold Neumaier

[Arnold Neumaier]

markwh04@yahoo.com wrote:

> himog wrote:
>
>>Is there a legitimate way to define a quantum state as some kind of
>>superposition of classical states?
>
> The quantum equivalent of a classical state is a coherent state; the
> process of arriving at a quantum theory which has the given classical
> state space as its classical limit is known more generally as Berezin
> quantization.

And every quantum state can be written as a superposition of coherent
states, though not in a unique way. Thus the view of quantums states as
superposition of classical (i.e., coherent) states is fully valid.

Of course, under a sufficiemtly nontrivial quantum dynamics,
a coherent state does not remain coherent as time develops;
this explains the departure from classicality in quantum mechanics.

In particular, typical nonlocal entanglement phenomena can be
viewed neatly in terms of superpositions of coherent states
which are spatially well separated.

Arnold Neumaier

[Arnold Neumaier]

markwh04@yahoo.com wrote:

> himog wrote:
>
>>Is there a legitimate way to define a quantum state as some kind of
>>superposition of classical states?
>
> The quantum equivalent of a classical state is a coherent state; the
> process of arriving at a quantum theory which has the given classical
> state space as its classical limit is known more generally as Berezin
> quantization.

And every quantum state can be written as a superposition of coherent
states, though not in a unique way. Thus the view of quantums states as
superposition of classical (i.e., coherent) states is fully valid.

Of course, under a sufficiemtly nontrivial quantum dynamics,
a coherent state does not remain coherent as time develops;
this explains the departure from classicality in quantum mechanics.

In particular, typical nonlocal entanglement phenomena can be
viewed neatly in terms of superpositions of coherent states
which are spatially well separated.

Arnold Neumaier

[Arnold Neumaier]

markwh04@yahoo.com wrote:

> himog wrote:
>
>>Is there a legitimate way to define a quantum state as some kind of
>>superposition of classical states?
>
> The quantum equivalent of a classical state is a coherent state; the
> process of arriving at a quantum theory which has the given classical
> state space as its classical limit is known more generally as Berezin
> quantization.

And every quantum state can be written as a superposition of coherent
states, though not in a unique way. Thus the view of quantums states as
superposition of classical (i.e., coherent) states is fully valid.

Of course, under a sufficiemtly nontrivial quantum dynamics,
a coherent state does not remain coherent as time develops;
this explains the departure from classicality in quantum mechanics.

In particular, typical nonlocal entanglement phenomena can be
viewed neatly in terms of superpositions of coherent states
which are spatially well separated.

Arnold Neumaier

[Arnold Neumaier]

markwh04@yahoo.com wrote:

> himog wrote:
>
>>Is there a legitimate way to define a quantum state as some kind of
>>superposition of classical states?
>
> The quantum equivalent of a classical state is a coherent state; the
> process of arriving at a quantum theory which has the given classical
> state space as its classical limit is known more generally as Berezin
> quantization.

And every quantum state can be written as a superposition of coherent
states, though not in a unique way. Thus the view of quantums states as
superposition of classical (i.e., coherent) states is fully valid.

Of course, under a sufficiemtly nontrivial quantum dynamics,
a coherent state does not remain coherent as time develops;
this explains the departure from classicality in quantum mechanics.

In particular, typical nonlocal entanglement phenomena can be
viewed neatly in terms of superpositions of coherent states
which are spatially well separated.

Arnold Neumaier

[jarek korbicz]

> And every quantum state can be written as a superposition of coherent
> states, though not in a unique way. Thus the view of quantums states as
> superposition of classical (i.e., coherent) states is fully valid.

The distinction between classical and quantum states can be very nicely
formalized when one looks at the general, i.e. mixed states of a
canonically quantized system. Then one finds that indeed there are
states which behave like classical (the only ad hoc assumption being
that one uses normally ordered operators when calculating averages). If
anybody wants to learn more about how to distinct those states, he may
want to take a look at Phys. Rev. Lett. 94, 153601 (2005)

> Of course, under a sufficiemtly nontrivial quantum dynamics,
> a coherent state does not remain coherent as time develops;
> this explains the departure from classicality in quantum mechanics.

To be more precise, only hamiltonians at most quadratic in x, p leave
coherent states invariant.

Best,
jarek

[jarek korbicz]

> And every quantum state can be written as a superposition of coherent
> states, though not in a unique way. Thus the view of quantums states as
> superposition of classical (i.e., coherent) states is fully valid.

The distinction between classical and quantum states can be very nicely
formalized when one looks at the general, i.e. mixed states of a
canonically quantized system. Then one finds that indeed there are
states which behave like classical (the only ad hoc assumption being
that one uses normally ordered operators when calculating averages). If
anybody wants to learn more about how to distinct those states, he may
want to take a look at Phys. Rev. Lett. 94, 153601 (2005)

> Of course, under a sufficiemtly nontrivial quantum dynamics,
> a coherent state does not remain coherent as time develops;
> this explains the departure from classicality in quantum mechanics.

To be more precise, only hamiltonians at most quadratic in x, p leave
coherent states invariant.

Best,
jarek

[jarek korbicz]

> And every quantum state can be written as a superposition of coherent
> states, though not in a unique way. Thus the view of quantums states as
> superposition of classical (i.e., coherent) states is fully valid.

The distinction between classical and quantum states can be very nicely
formalized when one looks at the general, i.e. mixed states of a
canonically quantized system. Then one finds that indeed there are
states which behave like classical (the only ad hoc assumption being
that one uses normally ordered operators when calculating averages). If
anybody wants to learn more about how to distinct those states, he may
want to take a look at Phys. Rev. Lett. 94, 153601 (2005)

> Of course, under a sufficiemtly nontrivial quantum dynamics,
> a coherent state does not remain coherent as time develops;
> this explains the departure from classicality in quantum mechanics.

To be more precise, only hamiltonians at most quadratic in x, p leave
coherent states invariant.

Best,
jarek

[jarek korbicz]

> And every quantum state can be written as a superposition of coherent
> states, though not in a unique way. Thus the view of quantums states as
> superposition of classical (i.e., coherent) states is fully valid.

The distinction between classical and quantum states can be very nicely
formalized when one looks at the general, i.e. mixed states of a
canonically quantized system. Then one finds that indeed there are
states which behave like classical (the only ad hoc assumption being
that one uses normally ordered operators when calculating averages). If
anybody wants to learn more about how to distinct those states, he may
want to take a look at Phys. Rev. Lett. 94, 153601 (2005)

> Of course, under a sufficiemtly nontrivial quantum dynamics,
> a coherent state does not remain coherent as time develops;
> this explains the departure from classicality in quantum mechanics.

To be more precise, only hamiltonians at most quadratic in x, p leave
coherent states invariant.

Best,
jarek

[jarek korbicz]

> And every quantum state can be written as a superposition of coherent
> states, though not in a unique way. Thus the view of quantums states as
> superposition of classical (i.e., coherent) states is fully valid.

The distinction between classical and quantum states can be very nicely
formalized when one looks at the general, i.e. mixed states of a
canonically quantized system. Then one finds that indeed there are
states which behave like classical (the only ad hoc assumption being
that one uses normally ordered operators when calculating averages). If
anybody wants to learn more about how to distinct those states, he may
want to take a look at Phys. Rev. Lett. 94, 153601 (2005)

> Of course, under a sufficiemtly nontrivial quantum dynamics,
> a coherent state does not remain coherent as time develops;
> this explains the departure from classicality in quantum mechanics.

To be more precise, only hamiltonians at most quadratic in x, p leave
coherent states invariant.

Best,
jarek

[jarek korbicz]

> And every quantum state can be written as a superposition of coherent
> states, though not in a unique way. Thus the view of quantums states as
> superposition of classical (i.e., coherent) states is fully valid.

The distinction between classical and quantum states can be very nicely
formalized when one looks at the general, i.e. mixed states of a
canonically quantized system. Then one finds that indeed there are
states which behave like classical (the only ad hoc assumption being
that one uses normally ordered operators when calculating averages). If
anybody wants to learn more about how to distinct those states, he may
want to take a look at Phys. Rev. Lett. 94, 153601 (2005)

> Of course, under a sufficiemtly nontrivial quantum dynamics,
> a coherent state does not remain coherent as time develops;
> this explains the departure from classicality in quantum mechanics.

To be more precise, only hamiltonians at most quadratic in x, p leave
coherent states invariant.

Best,
jarek

[jarek korbicz]

> And every quantum state can be written as a superposition of coherent
> states, though not in a unique way. Thus the view of quantums states as
> superposition of classical (i.e., coherent) states is fully valid.

The distinction between classical and quantum states can be very nicely
formalized when one looks at the general, i.e. mixed states of a
canonically quantized system. Then one finds that indeed there are
states which behave like classical (the only ad hoc assumption being
that one uses normally ordered operators when calculating averages). If
anybody wants to learn more about how to distinct those states, he may
want to take a look at Phys. Rev. Lett. 94, 153601 (2005)

> Of course, under a sufficiemtly nontrivial quantum dynamics,
> a coherent state does not remain coherent as time develops;
> this explains the departure from classicality in quantum mechanics.

To be more precise, only hamiltonians at most quadratic in x, p leave
coherent states invariant.

Best,
jarek

[jarek korbicz]

> And every quantum state can be written as a superposition of coherent
> states, though not in a unique way. Thus the view of quantums states as
> superposition of classical (i.e., coherent) states is fully valid.

The distinction between classical and quantum states can be very nicely
formalized when one looks at the general, i.e. mixed states of a
canonically quantized system. Then one finds that indeed there are
states which behave like classical (the only ad hoc assumption being
that one uses normally ordered operators when calculating averages). If
anybody wants to learn more about how to distinct those states, he may
want to take a look at Phys. Rev. Lett. 94, 153601 (2005)

> Of course, under a sufficiemtly nontrivial quantum dynamics,
> a coherent state does not remain coherent as time develops;
> this explains the departure from classicality in quantum mechanics.

To be more precise, only hamiltonians at most quadratic in x, p leave
coherent states invariant.

Best,
jarek

[jarek korbicz]

> And every quantum state can be written as a superposition of coherent
> states, though not in a unique way. Thus the view of quantums states as
> superposition of classical (i.e., coherent) states is fully valid.

The distinction between classical and quantum states can be very nicely
formalized when one looks at the general, i.e. mixed states of a
canonically quantized system. Then one finds that indeed there are
states which behave like classical (the only ad hoc assumption being
that one uses normally ordered operators when calculating averages). If
anybody wants to learn more about how to distinct those states, he may
want to take a look at Phys. Rev. Lett. 94, 153601 (2005)

> Of course, under a sufficiemtly nontrivial quantum dynamics,
> a coherent state does not remain coherent as time develops;
> this explains the departure from classicality in quantum mechanics.

To be more precise, only hamiltonians at most quadratic in x, p leave
coherent states invariant.

Best,
jarek

[Souvik]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

A quantum state may be viewed as the sum over all possible
almost-classical states.

Elucidation:

[Most people in this thread have looked at the Hamiltonian formalism of
quantum mechanics. However, I feel that though such time-evolution
formalism is practical, the Lagrangian formalism offers greater insight
and simpler interpretations.]

In the Lagrangian (or path integral formalism), a the state of an
object may be extended space and time (or all its possible degrees of
freedom). In hard-ball terms, you could define: 'A ball flying from
*this point* in spacetime to *that*' as a state. The 'quantum state'
for such an event/ trajectory would simply be the linear addition of
all paths that can lead the ball from point *this* to *that*,
classically allowable or not! The only catch is: you must weigh each
path with a weight of the form exp(i*S) where S is the classical
'Action' corresponding to each path. It turns out that the 'classical
path / trajectory / event / 4-D state' is the path with the heaviest
weight.

So it is alright to imagine a quantum state as a superposition of all
classical and neo-classical (and wild not-classically-allowed-at-all)
states, as long as you know how to weight your addition!

-Souvik

[Souvik]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

A quantum state may be viewed as the sum over all possible
almost-classical states.

Elucidation:

[Most people in this thread have looked at the Hamiltonian formalism of
quantum mechanics. However, I feel that though such time-evolution
formalism is practical, the Lagrangian formalism offers greater insight
and simpler interpretations.]

In the Lagrangian (or path integral formalism), a the state of an
object may be extended space and time (or all its possible degrees of
freedom). In hard-ball terms, you could define: 'A ball flying from
*this point* in spacetime to *that*' as a state. The 'quantum state'
for such an event/ trajectory would simply be the linear addition of
all paths that can lead the ball from point *this* to *that*,
classically allowable or not! The only catch is: you must weigh each
path with a weight of the form exp(i*S) where S is the classical
'Action' corresponding to each path. It turns out that the 'classical
path / trajectory / event / 4-D state' is the path with the heaviest
weight.

So it is alright to imagine a quantum state as a superposition of all
classical and neo-classical (and wild not-classically-allowed-at-all)
states, as long as you know how to weight your addition!

-Souvik

[Souvik]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

A quantum state may be viewed as the sum over all possible
almost-classical states.

Elucidation:

[Most people in this thread have looked at the Hamiltonian formalism of
quantum mechanics. However, I feel that though such time-evolution
formalism is practical, the Lagrangian formalism offers greater insight
and simpler interpretations.]

In the Lagrangian (or path integral formalism), a the state of an
object may be extended space and time (or all its possible degrees of
freedom). In hard-ball terms, you could define: 'A ball flying from
*this point* in spacetime to *that*' as a state. The 'quantum state'
for such an event/ trajectory would simply be the linear addition of
all paths that can lead the ball from point *this* to *that*,
classically allowable or not! The only catch is: you must weigh each
path with a weight of the form exp(i*S) where S is the classical
'Action' corresponding to each path. It turns out that the 'classical
path / trajectory / event / 4-D state' is the path with the heaviest
weight.

So it is alright to imagine a quantum state as a superposition of all
classical and neo-classical (and wild not-classically-allowed-at-all)
states, as long as you know how to weight your addition!

-Souvik

[Souvik]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

A quantum state may be viewed as the sum over all possible
almost-classical states.

Elucidation:

[Most people in this thread have looked at the Hamiltonian formalism of
quantum mechanics. However, I feel that though such time-evolution
formalism is practical, the Lagrangian formalism offers greater insight
and simpler interpretations.]

In the Lagrangian (or path integral formalism), a the state of an
object may be extended space and time (or all its possible degrees of
freedom). In hard-ball terms, you could define: 'A ball flying from
*this point* in spacetime to *that*' as a state. The 'quantum state'
for such an event/ trajectory would simply be the linear addition of
all paths that can lead the ball from point *this* to *that*,
classically allowable or not! The only catch is: you must weigh each
path with a weight of the form exp(i*S) where S is the classical
'Action' corresponding to each path. It turns out that the 'classical
path / trajectory / event / 4-D state' is the path with the heaviest
weight.

So it is alright to imagine a quantum state as a superposition of all
classical and neo-classical (and wild not-classically-allowed-at-all)
states, as long as you know how to weight your addition!

-Souvik

[Souvik]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

A quantum state may be viewed as the sum over all possible
almost-classical states.

Elucidation:

[Most people in this thread have looked at the Hamiltonian formalism of
quantum mechanics. However, I feel that though such time-evolution
formalism is practical, the Lagrangian formalism offers greater insight
and simpler interpretations.]

In the Lagrangian (or path integral formalism), a the state of an
object may be extended space and time (or all its possible degrees of
freedom). In hard-ball terms, you could define: 'A ball flying from
*this point* in spacetime to *that*' as a state. The 'quantum state'
for such an event/ trajectory would simply be the linear addition of
all paths that can lead the ball from point *this* to *that*,
classically allowable or not! The only catch is: you must weigh each
path with a weight of the form exp(i*S) where S is the classical
'Action' corresponding to each path. It turns out that the 'classical
path / trajectory / event / 4-D state' is the path with the heaviest
weight.

So it is alright to imagine a quantum state as a superposition of all
classical and neo-classical (and wild not-classically-allowed-at-all)
states, as long as you know how to weight your addition!

-Souvik

[Souvik]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

A quantum state may be viewed as the sum over all possible
almost-classical states.

Elucidation:

[Most people in this thread have looked at the Hamiltonian formalism of
quantum mechanics. However, I feel that though such time-evolution
formalism is practical, the Lagrangian formalism offers greater insight
and simpler interpretations.]

In the Lagrangian (or path integral formalism), a the state of an
object may be extended space and time (or all its possible degrees of
freedom). In hard-ball terms, you could define: 'A ball flying from
*this point* in spacetime to *that*' as a state. The 'quantum state'
for such an event/ trajectory would simply be the linear addition of
all paths that can lead the ball from point *this* to *that*,
classically allowable or not! The only catch is: you must weigh each
path with a weight of the form exp(i*S) where S is the classical
'Action' corresponding to each path. It turns out that the 'classical
path / trajectory / event / 4-D state' is the path with the heaviest
weight.

So it is alright to imagine a quantum state as a superposition of all
classical and neo-classical (and wild not-classically-allowed-at-all)
states, as long as you know how to weight your addition!

-Souvik

[Souvik]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

A quantum state may be viewed as the sum over all possible
almost-classical states.

Elucidation:

[Most people in this thread have looked at the Hamiltonian formalism of
quantum mechanics. However, I feel that though such time-evolution
formalism is practical, the Lagrangian formalism offers greater insight
and simpler interpretations.]

In the Lagrangian (or path integral formalism), a the state of an
object may be extended space and time (or all its possible degrees of
freedom). In hard-ball terms, you could define: 'A ball flying from
*this point* in spacetime to *that*' as a state. The 'quantum state'
for such an event/ trajectory would simply be the linear addition of
all paths that can lead the ball from point *this* to *that*,
classically allowable or not! The only catch is: you must weigh each
path with a weight of the form exp(i*S) where S is the classical
'Action' corresponding to each path. It turns out that the 'classical
path / trajectory / event / 4-D state' is the path with the heaviest
weight.

So it is alright to imagine a quantum state as a superposition of all
classical and neo-classical (and wild not-classically-allowed-at-all)
states, as long as you know how to weight your addition!

-Souvik

[Souvik]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

A quantum state may be viewed as the sum over all possible
almost-classical states.

Elucidation:

[Most people in this thread have looked at the Hamiltonian formalism of
quantum mechanics. However, I feel that though such time-evolution
formalism is practical, the Lagrangian formalism offers greater insight
and simpler interpretations.]

In the Lagrangian (or path integral formalism), a the state of an
object may be extended space and time (or all its possible degrees of
freedom). In hard-ball terms, you could define: 'A ball flying from
*this point* in spacetime to *that*' as a state. The 'quantum state'
for such an event/ trajectory would simply be the linear addition of
all paths that can lead the ball from point *this* to *that*,
classically allowable or not! The only catch is: you must weigh each
path with a weight of the form exp(i*S) where S is the classical
'Action' corresponding to each path. It turns out that the 'classical
path / trajectory / event / 4-D state' is the path with the heaviest
weight.

So it is alright to imagine a quantum state as a superposition of all
classical and neo-classical (and wild not-classically-allowed-at-all)
states, as long as you know how to weight your addition!

-Souvik

[Souvik]

himog wrote:
> Is there a legitimate way to define a quantum state as some kind of
> superposition of classical states?

A quantum state may be viewed as the sum over all possible
almost-classical states.

Elucidation:

[Most people in this thread have looked at the Hamiltonian formalism of
quantum mechanics. However, I feel that though such time-evolution
formalism is practical, the Lagrangian formalism offers greater insight
and simpler interpretations.]

In the Lagrangian (or path integral formalism), a the state of an
object may be extended space and time (or all its possible degrees of
freedom). In hard-ball terms, you could define: 'A ball flying from
*this point* in spacetime to *that*' as a state. The 'quantum state'
for such an event/ trajectory would simply be the linear addition of
all paths that can lead the ball from point *this* to *that*,
classically allowable or not! The only catch is: you must weigh each
path with a weight of the form exp(i*S) where S is the classical
'Action' corresponding to each path. It turns out that the 'classical
path / trajectory / event / 4-D state' is the path with the heaviest
weight.

So it is alright to imagine a quantum state as a superposition of all
classical and neo-classical (and wild not-classically-allowed-at-all)
states, as long as you know how to weight your addition!

-Souvik

[C. M. Heard]

himog asked:
> Is there a legitimate way to define a quantum state as some
> kind of superposition of classical states?

Dr. Paul Kinsler replied:
> You might find it interesting to have a look at the
> Wigner distribution.

"jarek korbicz" wrote:
> Arnold Neumaier wrote:
> > markwh04@yahoo.com wrote:
> > > The quantum equivalent of a classical state is a coherent state; the
> > > process of arriving at a quantum theory which has the given classical
> > > state space as its classical limit is known more generally as Berezin
> > > quantization.
> >
> > And every quantum state can be written as a superposition of coherent
> > states, though not in a unique way. Thus the view of quantums states as
> > superposition of classical (i.e., coherent) states is fully valid.
>
> The distinction between classical and quantum states can be very nicely
> formalized when one looks at the general, i.e. mixed states of a
> canonically quantized system. Then one finds that indeed there are
> states which behave like classical (the only ad hoc assumption being
> that one uses normally ordered operators when calculating averages). If
> anybody wants to learn more about how to distinct those states, he may
> want to take a look at Phys. Rev. Lett. 94, 153601 (2005)

This sounds interesting. If you can give an equivalent Arxiv preprint
reference that would be appreciated.

In the meantime, allow me to point out that with a different ad-hoc
assumption -- namely, that one uses symmetrically ordered operators when
calculating averages -- one finds that the quantum states that "behave
clasically" are precisely those with positive Wigner distributions.

> > Of course, under a sufficiemtly nontrivial quantum dynamics,
> > a coherent state does not remain coherent as time develops;
> > this explains the departure from classicality in quantum mechanics.
>
> To be more precise, only hamiltonians at most quadratic in x, p leave
> coherent states invariant.

And -- for pure states -- it is precisely these Hamiltonians that
generate unitary transformations that leave the property of having
a positive Wigner distribution unaltered. These transformations are
just linear canonical transformations. The pure states with positive
Wigner distributions include coherent states, squeezed coherent states,
and (if one allows the term "state" to be abused somewhat) states with
a definite value of Ux + Vp where U and V are real c-numbers.

//cmh

[C. M. Heard]

himog asked:
> Is there a legitimate way to define a quantum state as some
> kind of superposition of classical states?

Dr. Paul Kinsler replied:
> You might find it interesting to have a look at the
> Wigner distribution.

"jarek korbicz" wrote:
> Arnold Neumaier wrote:
> > markwh04@yahoo.com wrote:
> > > The quantum equivalent of a classical state is a coherent state; the
> > > process of arriving at a quantum theory which has the given classical
> > > state space as its classical limit is known more generally as Berezin
> > > quantization.
> >
> > And every quantum state can be written as a superposition of coherent
> > states, though not in a unique way. Thus the view of quantums states as
> > superposition of classical (i.e., coherent) states is fully valid.
>
> The distinction between classical and quantum states can be very nicely
> formalized when one looks at the general, i.e. mixed states of a
> canonically quantized system. Then one finds that indeed there are
> states which behave like classical (the only ad hoc assumption being
> that one uses normally ordered operators when calculating averages). If
> anybody wants to learn more about how to distinct those states, he may
> want to take a look at Phys. Rev. Lett. 94, 153601 (2005)

This sounds interesting. If you can give an equivalent Arxiv preprint
reference that would be appreciated.

In the meantime, allow me to point out that with a different ad-hoc
assumption -- namely, that one uses symmetrically ordered operators when
calculating averages -- one finds that the quantum states that "behave
clasically" are precisely those with positive Wigner distributions.

> > Of course, under a sufficiemtly nontrivial quantum dynamics,
> > a coherent state does not remain coherent as time develops;
> > this explains the departure from classicality in quantum mechanics.
>
> To be more precise, only hamiltonians at most quadratic in x, p leave
> coherent states invariant.

And -- for pure states -- it is precisely these Hamiltonians that
generate unitary transformations that leave the property of having
a positive Wigner distribution unaltered. These transformations are
just linear canonical transformations. The pure states with positive
Wigner distributions include coherent states, squeezed coherent states,
and (if one allows the term "state" to be abused somewhat) states with
a definite value of Ux + Vp where U and V are real c-numbers.

//cmh

[C. M. Heard]

himog asked:
> Is there a legitimate way to define a quantum state as some
> kind of superposition of classical states?

Dr. Paul Kinsler replied:
> You might find it interesting to have a look at the
> Wigner distribution.

"jarek korbicz" wrote:
> Arnold Neumaier wrote:
> > markwh04@yahoo.com wrote:
> > > The quantum equivalent of a classical state is a coherent state; the
> > > process of arriving at a quantum theory which has the given classical
> > > state space as its classical limit is known more generally as Berezin
> > > quantization.
> >
> > And every quantum state can be written as a superposition of coherent
> > states, though not in a unique way. Thus the view of quantums states as
> > superposition of classical (i.e., coherent) states is fully valid.
>
> The distinction between classical and quantum states can be very nicely
> formalized when one looks at the general, i.e. mixed states of a
> canonically quantized system. Then one finds that indeed there are
> states which behave like classical (the only ad hoc assumption being
> that one uses normally ordered operators when calculating averages). If
> anybody wants to learn more about how to distinct those states, he may
> want to take a look at Phys. Rev. Lett. 94, 153601 (2005)

This sounds interesting. If you can give an equivalent Arxiv preprint
reference that would be appreciated.

In the meantime, allow me to point out that with a different ad-hoc
assumption -- namely, that one uses symmetrically ordered operators when
calculating averages -- one finds that the quantum states that "behave
clasically" are precisely those with positive Wigner distributions.

> > Of course, under a sufficiemtly nontrivial quantum dynamics,
> > a coherent state does not remain coherent as time develops;
> > this explains the departure from classicality in quantum mechanics.
>
> To be more precise, only hamiltonians at most quadratic in x, p leave
> coherent states invariant.

And -- for pure states -- it is precisely these Hamiltonians that
generate unitary transformations that leave the property of having
a positive Wigner distribution unaltered. These transformations are
just linear canonical transformations. The pure states with positive
Wigner distributions include coherent states, squeezed coherent states,
and (if one allows the term "state" to be abused somewhat) states with
a definite value of Ux + Vp where U and V are real c-numbers.

//cmh

[C. M. Heard]

himog asked:
> Is there a legitimate way to define a quantum state as some
> kind of superposition of classical states?

Dr. Paul Kinsler replied:
> You might find it interesting to have a look at the
> Wigner distribution.

"jarek korbicz" wrote:
> Arnold Neumaier wrote:
> > markwh04@yahoo.com wrote:
> > > The quantum equivalent of a classical state is a coherent state; the
> > > process of arriving at a quantum theory which has the given classical
> > > state space as its classical limit is known more generally as Berezin
> > > quantization.
> >
> > And every quantum state can be written as a superposition of coherent
> > states, though not in a unique way. Thus the view of quantums states as
> > superposition of classical (i.e., coherent) states is fully valid.
>
> The distinction between classical and quantum states can be very nicely
> formalized when one looks at the general, i.e. mixed states of a
> canonically quantized system. Then one finds that indeed there are
> states which behave like classical (the only ad hoc assumption being
> that one uses normally ordered operators when calculating averages). If
> anybody wants to learn more about how to distinct those states, he may
> want to take a look at Phys. Rev. Lett. 94, 153601 (2005)

This sounds interesting. If you can give an equivalent Arxiv preprint
reference that would be appreciated.

In the meantime, allow me to point out that with a different ad-hoc
assumption -- namely, that one uses symmetrically ordered operators when
calculating averages -- one finds that the quantum states that "behave
clasically" are precisely those with positive Wigner distributions.

> > Of course, under a sufficiemtly nontrivial quantum dynamics,
> > a coherent state does not remain coherent as time develops;
> > this explains the departure from classicality in quantum mechanics.
>
> To be more precise, only hamiltonians at most quadratic in x, p leave
> coherent states invariant.

And -- for pure states -- it is precisely these Hamiltonians that
generate unitary transformations that leave the property of having
a positive Wigner distribution unaltered. These transformations are
just linear canonical transformations. The pure states with positive
Wigner distributions include coherent states, squeezed coherent states,
and (if one allows the term "state" to be abused somewhat) states with
a definite value of Ux + Vp where U and V are real c-numbers.

//cmh

[C. M. Heard]

himog asked:
> Is there a legitimate way to define a quantum state as some
> kind of superposition of classical states?

Dr. Paul Kinsler replied:
> You might find it interesting to have a look at the
> Wigner distribution.

"jarek korbicz" wrote:
> Arnold Neumaier wrote:
> > markwh04@yahoo.com wrote:
> > > The quantum equivalent of a classical state is a coherent state; the
> > > process of arriving at a quantum theory which has the given classical
> > > state space as its classical limit is known more generally as Berezin
> > > quantization.
> >
> > And every quantum state can be written as a superposition of coherent
> > states, though not in a unique way. Thus the view of quantums states as
> > superposition of classical (i.e., coherent) states is fully valid.
>
> The distinction between classical and quantum states can be very nicely
> formalized when one looks at the general, i.e. mixed states of a
> canonically quantized system. Then one finds that indeed there are
> states which behave like classical (the only ad hoc assumption being
> that one uses normally ordered operators when calculating averages). If
> anybody wants to learn more about how to distinct those states, he may
> want to take a look at Phys. Rev. Lett. 94, 153601 (2005)

This sounds interesting. If you can give an equivalent Arxiv preprint
reference that would be appreciated.

In the meantime, allow me to point out that with a different ad-hoc
assumption -- namely, that one uses symmetrically ordered operators when
calculating averages -- one finds that the quantum states that "behave
clasically" are precisely those with positive Wigner distributions.

> > Of course, under a sufficiemtly nontrivial quantum dynamics,
> > a coherent state does not remain coherent as time develops;
> > this explains the departure from classicality in quantum mechanics.
>
> To be more precise, only hamiltonians at most quadratic in x, p leave
> coherent states invariant.

And -- for pure states -- it is precisely these Hamiltonians that
generate unitary transformations that leave the property of having
a positive Wigner distribution unaltered. These transformations are
just linear canonical transformations. The pure states with positive
Wigner distributions include coherent states, squeezed coherent states,
and (if one allows the term "state" to be abused somewhat) states with
a definite value of Ux + Vp where U and V are real c-numbers.

//cmh

[C. M. Heard]

himog asked:
> Is there a legitimate way to define a quantum state as some
> kind of superposition of classical states?

Dr. Paul Kinsler replied:
> You might find it interesting to have a look at the
> Wigner distribution.

"jarek korbicz" wrote:
> Arnold Neumaier wrote:
> > markwh04@yahoo.com wrote:
> > > The quantum equivalent of a classical state is a coherent state; the
> > > process of arriving at a quantum theory which has the given classical
> > > state space as its classical limit is known more generally as Berezin
> > > quantization.
> >
> > And every quantum state can be written as a superposition of coherent
> > states, though not in a unique way. Thus the view of quantums states as
> > superposition of classical (i.e., coherent) states is fully valid.
>
> The distinction between classical and quantum states can be very nicely
> formalized when one looks at the general, i.e. mixed states of a
> canonically quantized system. Then one finds that indeed there are
> states which behave like classical (the only ad hoc assumption being
> that one uses normally ordered operators when calculating averages). If
> anybody wants to learn more about how to distinct those states, he may
> want to take a look at Phys. Rev. Lett. 94, 153601 (2005)

This sounds interesting. If you can give an equivalent Arxiv preprint
reference that would be appreciated.

In the meantime, allow me to point out that with a different ad-hoc
assumption -- namely, that one uses symmetrically ordered operators when
calculating averages -- one finds that the quantum states that "behave
clasically" are precisely those with positive Wigner distributions.

> > Of course, under a sufficiemtly nontrivial quantum dynamics,
> > a coherent state does not remain coherent as time develops;
> > this explains the departure from classicality in quantum mechanics.
>
> To be more precise, only hamiltonians at most quadratic in x, p leave
> coherent states invariant.

And -- for pure states -- it is precisely these Hamiltonians that
generate unitary transformations that leave the property of having
a positive Wigner distribution unaltered. These transformations are
just linear canonical transformations. The pure states with positive
Wigner distributions include coherent states, squeezed coherent states,
and (if one allows the term "state" to be abused somewhat) states with
a definite value of Ux + Vp where U and V are real c-numbers.

//cmh

[C. M. Heard]

himog asked:
> Is there a legitimate way to define a quantum state as some
> kind of superposition of classical states?

Dr. Paul Kinsler replied:
> You might find it interesting to have a look at the
> Wigner distribution.

"jarek korbicz" wrote:
> Arnold Neumaier wrote:
> > markwh04@yahoo.com wrote:
> > > The quantum equivalent of a classical state is a coherent state; the
> > > process of arriving at a quantum theory which has the given classical
> > > state space as its classical limit is known more generally as Berezin
> > > quantization.
> >
> > And every quantum state can be written as a superposition of coherent
> > states, though not in a unique way. Thus the view of quantums states as
> > superposition of classical (i.e., coherent) states is fully valid.
>
> The distinction between classical and quantum states can be very nicely
> formalized when one looks at the general, i.e. mixed states of a
> canonically quantized system. Then one finds that indeed there are
> states which behave like classical (the only ad hoc assumption being
> that one uses normally ordered operators when calculating averages). If
> anybody wants to learn more about how to distinct those states, he may
> want to take a look at Phys. Rev. Lett. 94, 153601 (2005)

This sounds interesting. If you can give an equivalent Arxiv preprint
reference that would be appreciated.

In the meantime, allow me to point out that with a different ad-hoc
assumption -- namely, that one uses symmetrically ordered operators when
calculating averages -- one finds that the quantum states that "behave
clasically" are precisely those with positive Wigner distributions.

> > Of course, under a sufficiemtly nontrivial quantum dynamics,
> > a coherent state does not remain coherent as time develops;
> > this explains the departure from classicality in quantum mechanics.
>
> To be more precise, only hamiltonians at most quadratic in x, p leave
> coherent states invariant.

And -- for pure states -- it is precisely these Hamiltonians that
generate unitary transformations that leave the property of having
a positive Wigner distribution unaltered. These transformations are
just linear canonical transformations. The pure states with positive
Wigner distributions include coherent states, squeezed coherent states,
and (if one allows the term "state" to be abused somewhat) states with
a definite value of Ux + Vp where U and V are real c-numbers.

//cmh

[C. M. Heard]

himog asked:
> Is there a legitimate way to define a quantum state as some
> kind of superposition of classical states?

Dr. Paul Kinsler replied:
> You might find it interesting to have a look at the
> Wigner distribution.

"jarek korbicz" wrote:
> Arnold Neumaier wrote:
> > markwh04@yahoo.com wrote:
> > > The quantum equivalent of a classical state is a coherent state; the
> > > process of arriving at a quantum theory which has the given classical
> > > state space as its classical limit is known more generally as Berezin
> > > quantization.
> >
> > And every quantum state can be written as a superposition of coherent
> > states, though not in a unique way. Thus the view of quantums states as
> > superposition of classical (i.e., coherent) states is fully valid.
>
> The distinction between classical and quantum states can be very nicely
> formalized when one looks at the general, i.e. mixed states of a
> canonically quantized system. Then one finds that indeed there are
> states which behave like classical (the only ad hoc assumption being
> that one uses normally ordered operators when calculating averages). If
> anybody wants to learn more about how to distinct those states, he may
> want to take a look at Phys. Rev. Lett. 94, 153601 (2005)

This sounds interesting. If you can give an equivalent Arxiv preprint
reference that would be appreciated.

In the meantime, allow me to point out that with a different ad-hoc
assumption -- namely, that one uses symmetrically ordered operators when
calculating averages -- one finds that the quantum states that "behave
clasically" are precisely those with positive Wigner distributions.

> > Of course, under a sufficiemtly nontrivial quantum dynamics,
> > a coherent state does not remain coherent as time develops;
> > this explains the departure from classicality in quantum mechanics.
>
> To be more precise, only hamiltonians at most quadratic in x, p leave
> coherent states invariant.

And -- for pure states -- it is precisely these Hamiltonians that
generate unitary transformations that leave the property of having
a positive Wigner distribution unaltered. These transformations are
just linear canonical transformations. The pure states with positive
Wigner distributions include coherent states, squeezed coherent states,
and (if one allows the term "state" to be abused somewhat) states with
a definite value of Ux + Vp where U and V are real c-numbers.

//cmh

[C. M. Heard]

himog asked:
> Is there a legitimate way to define a quantum state as some
> kind of superposition of classical states?

Dr. Paul Kinsler replied:
> You might find it interesting to have a look at the
> Wigner distribution.

"jarek korbicz" wrote:
> Arnold Neumaier wrote:
> > markwh04@yahoo.com wrote:
> > > The quantum equivalent of a classical state is a coherent state; the
> > > process of arriving at a quantum theory which has the given classical
> > > state space as its classical limit is known more generally as Berezin
> > > quantization.
> >
> > And every quantum state can be written as a superposition of coherent
> > states, though not in a unique way. Thus the view of quantums states as
> > superposition of classical (i.e., coherent) states is fully valid.
>
> The distinction between classical and quantum states can be very nicely
> formalized when one looks at the general, i.e. mixed states of a
> canonically quantized system. Then one finds that indeed there are
> states which behave like classical (the only ad hoc assumption being
> that one uses normally ordered operators when calculating averages). If
> anybody wants to learn more about how to distinct those states, he may
> want to take a look at Phys. Rev. Lett. 94, 153601 (2005)

This sounds interesting. If you can give an equivalent Arxiv preprint
reference that would be appreciated.

In the meantime, allow me to point out that with a different ad-hoc
assumption -- namely, that one uses symmetrically ordered operators when
calculating averages -- one finds that the quantum states that "behave
clasically" are precisely those with positive Wigner distributions.

> > Of course, under a sufficiemtly nontrivial quantum dynamics,
> > a coherent state does not remain coherent as time develops;
> > this explains the departure from classicality in quantum mechanics.
>
> To be more precise, only hamiltonians at most quadratic in x, p leave
> coherent states invariant.

And -- for pure states -- it is precisely these Hamiltonians that
generate unitary transformations that leave the property of having
a positive Wigner distribution unaltered. These transformations are
just linear canonical transformations. The pure states with positive
Wigner distributions include coherent states, squeezed coherent states,
and (if one allows the term "state" to be abused somewhat) states with
a definite value of Ux + Vp where U and V are real c-numbers.

//cmh

[himog]

Thank you all for the helpful responses.

Here's another question I came up with while thinking about this
thread:

In the one dimensional Shroedinger picture, one has two Fourier dual
wavefunctions for a particle, namely Psi(x,t) and Phi(p,t). Can one
derive these wavefunctions uniquely only given the probability
distributions Psi*Psi and Phi*Phi? My first guess is "no."

[himog]

Thank you all for the helpful responses.

Here's another question I came up with while thinking about this
thread:

In the one dimensional Shroedinger picture, one has two Fourier dual
wavefunctions for a particle, namely Psi(x,t) and Phi(p,t). Can one
derive these wavefunctions uniquely only given the probability
distributions Psi*Psi and Phi*Phi? My first guess is "no."

[himog]

Thank you all for the helpful responses.

Here's another question I came up with while thinking about this
thread:

In the one dimensional Shroedinger picture, one has two Fourier dual
wavefunctions for a particle, namely Psi(x,t) and Phi(p,t). Can one
derive these wavefunctions uniquely only given the probability
distributions Psi*Psi and Phi*Phi? My first guess is "no."

[himog]

Thank you all for the helpful responses.

Here's another question I came up with while thinking about this
thread:

In the one dimensional Shroedinger picture, one has two Fourier dual
wavefunctions for a particle, namely Psi(x,t) and Phi(p,t). Can one
derive these wavefunctions uniquely only given the probability
distributions Psi*Psi and Phi*Phi? My first guess is "no."

[himog]

Thank you all for the helpful responses.

Here's another question I came up with while thinking about this
thread:

In the one dimensional Shroedinger picture, one has two Fourier dual
wavefunctions for a particle, namely Psi(x,t) and Phi(p,t). Can one
derive these wavefunctions uniquely only given the probability
distributions Psi*Psi and Phi*Phi? My first guess is "no."

[himog]

Thank you all for the helpful responses.

Here's another question I came up with while thinking about this
thread:

In the one dimensional Shroedinger picture, one has two Fourier dual
wavefunctions for a particle, namely Psi(x,t) and Phi(p,t). Can one
derive these wavefunctions uniquely only given the probability
distributions Psi*Psi and Phi*Phi? My first guess is "no."

[himog]

Thank you all for the helpful responses.

Here's another question I came up with while thinking about this
thread:

In the one dimensional Shroedinger picture, one has two Fourier dual
wavefunctions for a particle, namely Psi(x,t) and Phi(p,t). Can one
derive these wavefunctions uniquely only given the probability
distributions Psi*Psi and Phi*Phi? My first guess is "no."

[himog]

Thank you all for the helpful responses.

Here's another question I came up with while thinking about this
thread:

In the one dimensional Shroedinger picture, one has two Fourier dual
wavefunctions for a particle, namely Psi(x,t) and Phi(p,t). Can one
derive these wavefunctions uniquely only given the probability
distributions Psi*Psi and Phi*Phi? My first guess is "no."

[himog]

Thank you all for the helpful responses.

Here's another question I came up with while thinking about this
thread:

In the one dimensional Shroedinger picture, one has two Fourier dual
wavefunctions for a particle, namely Psi(x,t) and Phi(p,t). Can one
derive these wavefunctions uniquely only given the probability
distributions Psi*Psi and Phi*Phi? My first guess is "no."

[jarek korbicz]

> > If
> > anybody wants to learn more about how to distinct those states, he may
> > want to take a look at Phys. Rev. Lett. 94, 153601 (2005)
>
> This sounds interesting. If you can give an equivalent Arxiv preprint
> reference that would be appreciated.

Sure, it´s quant-ph/0408029

> In the meantime, allow me to point out that with a different ad-hoc
> assumption -- namely, that one uses symmetrically ordered operators when
> calculating averages -- one finds that the quantum states that "behave
> clasically" are precisely those with positive Wigner distributions.

At a first glance it seemed dissapointing to me that the property of
"being classical" depends on the ordering (we have chosen normal as the
most commonly used), but at the end why there should be just one way of
embedding classical statistics into quantum? Why there should be such
an embedding at all? the most important thing is to receive classical
statistics in the limit \hbar -> 0. I´m prepearing a short paper on
that.

> > To be more precise, only hamiltonians at most quadratic in x, p leave
> > coherent states invariant.

> And -- for pure states -- it is precisely these Hamiltonians that
> generate unitary transformations that leave the property of having
> a positive Wigner distribution unaltered. These transformations are
> just linear canonical transformations.

Yes, the quadratic hamiltonians generate the representation of the
metaplectic group - a universal double cover of the symplectic group.

> The pure states with positive
> Wigner distributions include coherent states, squeezed coherent states,
> and (if one allows the term "state" to be abused somewhat) states with
> a definite value of Ux + Vp where U and V are real c-numbers.

Let me just, very gently (dont want to go into wars :-), remark that
squeezing may be rather regarded as a manifestation of a quantum
property. A more or less systematic way of treating squeezing as a
signature of entanglement for finite systems may be found here:
quant-ph/0504005 and Refs. therein.

Best,
jarek

[jarek korbicz]

> > If
> > anybody wants to learn more about how to distinct those states, he may
> > want to take a look at Phys. Rev. Lett. 94, 153601 (2005)
>
> This sounds interesting. If you can give an equivalent Arxiv preprint
> reference that would be appreciated.

Sure, it´s quant-ph/0408029

> In the meantime, allow me to point out that with a different ad-hoc
> assumption -- namely, that one uses symmetrically ordered operators when
> calculating averages -- one finds that the quantum states that "behave
> clasically" are precisely those with positive Wigner distributions.

At a first glance it seemed dissapointing to me that the property of
"being classical" depends on the ordering (we have chosen normal as the
most commonly used), but at the end why there should be just one way of
embedding classical statistics into quantum? Why there should be such
an embedding at all? the most important thing is to receive classical
statistics in the limit \hbar -> 0. I´m prepearing a short paper on
that.

> > To be more precise, only hamiltonians at most quadratic in x, p leave
> > coherent states invariant.

> And -- for pure states -- it is precisely these Hamiltonians that
> generate unitary transformations that leave the property of having
> a positive Wigner distribution unaltered. These transformations are
> just linear canonical transformations.

Yes, the quadratic hamiltonians generate the representation of the
metaplectic group - a universal double cover of the symplectic group.

> The pure states with positive
> Wigner distributions include coherent states, squeezed coherent states,
> and (if one allows the term "state" to be abused somewhat) states with
> a definite value of Ux + Vp where U and V are real c-numbers.

Let me just, very gently (dont want to go into wars :-), remark that
squeezing may be rather regarded as a manifestation of a quantum
property. A more or less systematic way of treating squeezing as a
signature of entanglement for finite systems may be found here:
quant-ph/0504005 and Refs. therein.

Best,
jarek

[jarek korbicz]

> > If
> > anybody wants to learn more about how to distinct those states, he may
> > want to take a look at Phys. Rev. Lett. 94, 153601 (2005)
>
> This sounds interesting. If you can give an equivalent Arxiv preprint
> reference that would be appreciated.

Sure, it´s quant-ph/0408029

> In the meantime, allow me to point out that with a different ad-hoc
> assumption -- namely, that one uses symmetrically ordered operators when
> calculating averages -- one finds that the quantum states that "behave
> clasically" are precisely those with positive Wigner distributions.

At a first glance it seemed dissapointing to me that the property of
"being classical" depends on the ordering (we have chosen normal as the
most commonly used), but at the end why there should be just one way of
embedding classical statistics into quantum? Why there should be such
an embedding at all? the most important thing is to receive classical
statistics in the limit \hbar -> 0. I´m prepearing a short paper on
that.

> > To be more precise, only hamiltonians at most quadratic in x, p leave
> > coherent states invariant.

> And -- for pure states -- it is precisely these Hamiltonians that
> generate unitary transformations that leave the property of having
> a positive Wigner distribution unaltered. These transformations are
> just linear canonical transformations.

Yes, the quadratic hamiltonians generate the representation of the
metaplectic group - a universal double cover of the symplectic group.

> The pure states with positive
> Wigner distributions include coherent states, squeezed coherent states,
> and (if one allows the term "state" to be abused somewhat) states with
> a definite value of Ux + Vp where U and V are real c-numbers.

Let me just, very gently (dont want to go into wars :-), remark that
squeezing may be rather regarded as a manifestation of a quantum
property. A more or less systematic way of treating squeezing as a
signature of entanglement for finite systems may be found here:
quant-ph/0504005 and Refs. therein.

Best,
jarek

[jarek korbicz]

> > If
> > anybody wants to learn more about how to distinct those states, he may
> > want to take a look at Phys. Rev. Lett. 94, 153601 (2005)
>
> This sounds interesting. If you can give an equivalent Arxiv preprint
> reference that would be appreciated.

Sure, it´s quant-ph/0408029

> In the meantime, allow me to point out that with a different ad-hoc
> assumption -- namely, that one uses symmetrically ordered operators when
> calculating averages -- one finds that the quantum states that "behave
> clasically" are precisely those with positive Wigner distributions.

At a first glance it seemed dissapointing to me that the property of
"being classical" depends on the ordering (we have chosen normal as the
most commonly used), but at the end why there should be just one way of
embedding classical statistics into quantum? Why there should be such
an embedding at all? the most important thing is to receive classical
statistics in the limit \hbar -> 0. I´m prepearing a short paper on
that.

> > To be more precise, only hamiltonians at most quadratic in x, p leave
> > coherent states invariant.

> And -- for pure states -- it is precisely these Hamiltonians that
> generate unitary transformations that leave the property of having
> a positive Wigner distribution unaltered. These transformations are
> just linear canonical transformations.

Yes, the quadratic hamiltonians generate the representation of the
metaplectic group - a universal double cover of the symplectic group.

> The pure states with positive
> Wigner distributions include coherent states, squeezed coherent states,
> and (if one allows the term "state" to be abused somewhat) states with
> a definite value of Ux + Vp where U and V are real c-numbers.

Let me just, very gently (dont want to go into wars :-), remark that
squeezing may be rather regarded as a manifestation of a quantum
property. A more or less systematic way of treating squeezing as a
signature of entanglement for finite systems may be found here:
quant-ph/0504005 and Refs. therein.

Best,
jarek

[jarek korbicz]

> > If
> > anybody wants to learn more about how to distinct those states, he may
> > want to take a look at Phys. Rev. Lett. 94, 153601 (2005)
>
> This sounds interesting. If you can give an equivalent Arxiv preprint
> reference that would be appreciated.

Sure, it´s quant-ph/0408029

> In the meantime, allow me to point out that with a different ad-hoc
> assumption -- namely, that one uses symmetrically ordered operators when
> calculating averages -- one finds that the quantum states that "behave
> clasically" are precisely those with positive Wigner distributions.

At a first glance it seemed dissapointing to me that the property of
"being classical" depends on the ordering (we have chosen normal as the
most commonly used), but at the end why there should be just one way of
embedding classical statistics into quantum? Why there should be such
an embedding at all? the most important thing is to receive classical
statistics in the limit \hbar -> 0. I´m prepearing a short paper on
that.

> > To be more precise, only hamiltonians at most quadratic in x, p leave
> > coherent states invariant.

> And -- for pure states -- it is precisely these Hamiltonians that
> generate unitary transformations that leave the property of having
> a positive Wigner distribution unaltered. These transformations are
> just linear canonical transformations.

Yes, the quadratic hamiltonians generate the representation of the
metaplectic group - a universal double cover of the symplectic group.

> The pure states with positive
> Wigner distributions include coherent states, squeezed coherent states,
> and (if one allows the term "state" to be abused somewhat) states with
> a definite value of Ux + Vp where U and V are real c-numbers.

Let me just, very gently (dont want to go into wars :-), remark that
squeezing may be rather regarded as a manifestation of a quantum
property. A more or less systematic way of treating squeezing as a
signature of entanglement for finite systems may be found here:
quant-ph/0504005 and Refs. therein.

Best,
jarek

[jarek korbicz]

> > If
> > anybody wants to learn more about how to distinct those states, he may
> > want to take a look at Phys. Rev. Lett. 94, 153601 (2005)
>
> This sounds interesting. If you can give an equivalent Arxiv preprint
> reference that would be appreciated.

Sure, it´s quant-ph/0408029

> In the meantime, allow me to point out that with a different ad-hoc
> assumption -- namely, that one uses symmetrically ordered operators when
> calculating averages -- one finds that the quantum states that "behave
> clasically" are precisely those with positive Wigner distributions.

At a first glance it seemed dissapointing to me that the property of
"being classical" depends on the ordering (we have chosen normal as the
most commonly used), but at the end why there should be just one way of
embedding classical statistics into quantum? Why there should be such
an embedding at all? the most important thing is to receive classical
statistics in the limit \hbar -> 0. I´m prepearing a short paper on
that.

> > To be more precise, only hamiltonians at most quadratic in x, p leave
> > coherent states invariant.

> And -- for pure states -- it is precisely these Hamiltonians that
> generate unitary transformations that leave the property of having
> a positive Wigner distribution unaltered. These transformations are
> just linear canonical transformations.

Yes, the quadratic hamiltonians generate the representation of the
metaplectic group - a universal double cover of the symplectic group.

> The pure states with positive
> Wigner distributions include coherent states, squeezed coherent states,
> and (if one allows the term "state" to be abused somewhat) states with
> a definite value of Ux + Vp where U and V are real c-numbers.

Let me just, very gently (dont want to go into wars :-), remark that
squeezing may be rather regarded as a manifestation of a quantum
property. A more or less systematic way of treating squeezing as a
signature of entanglement for finite systems may be found here:
quant-ph/0504005 and Refs. therein.

Best,
jarek

[jarek korbicz]

> > If
> > anybody wants to learn more about how to distinct those states, he may
> > want to take a look at Phys. Rev. Lett. 94, 153601 (2005)
>
> This sounds interesting. If you can give an equivalent Arxiv preprint
> reference that would be appreciated.

Sure, it´s quant-ph/0408029

> In the meantime, allow me to point out that with a different ad-hoc
> assumption -- namely, that one uses symmetrically ordered operators when
> calculating averages -- one finds that the quantum states that "behave
> clasically" are precisely those with positive Wigner distributions.

At a first glance it seemed dissapointing to me that the property of
"being classical" depends on the ordering (we have chosen normal as the
most commonly used), but at the end why there should be just one way of
embedding classical statistics into quantum? Why there should be such
an embedding at all? the most important thing is to receive classical
statistics in the limit \hbar -> 0. I´m prepearing a short paper on
that.

> > To be more precise, only hamiltonians at most quadratic in x, p leave
> > coherent states invariant.

> And -- for pure states -- it is precisely these Hamiltonians that
> generate unitary transformations that leave the property of having
> a positive Wigner distribution unaltered. These transformations are
> just linear canonical transformations.

Yes, the quadratic hamiltonians generate the representation of the
metaplectic group - a universal double cover of the symplectic group.

> The pure states with positive
> Wigner distributions include coherent states, squeezed coherent states,
> and (if one allows the term "state" to be abused somewhat) states with
> a definite value of Ux + Vp where U and V are real c-numbers.

Let me just, very gently (dont want to go into wars :-), remark that
squeezing may be rather regarded as a manifestation of a quantum
property. A more or less systematic way of treating squeezing as a
signature of entanglement for finite systems may be found here:
quant-ph/0504005 and Refs. therein.

Best,
jarek

[jarek korbicz]

> > If
> > anybody wants to learn more about how to distinct those states, he may
> > want to take a look at Phys. Rev. Lett. 94, 153601 (2005)
>
> This sounds interesting. If you can give an equivalent Arxiv preprint
> reference that would be appreciated.

Sure, it´s quant-ph/0408029

> In the meantime, allow me to point out that with a different ad-hoc
> assumption -- namely, that one uses symmetrically ordered operators when
> calculating averages -- one finds that the quantum states that "behave
> clasically" are precisely those with positive Wigner distributions.

At a first glance it seemed dissapointing to me that the property of
"being classical" depends on the ordering (we have chosen normal as the
most commonly used), but at the end why there should be just one way of
embedding classical statistics into quantum? Why there should be such
an embedding at all? the most important thing is to receive classical
statistics in the limit \hbar -> 0. I´m prepearing a short paper on
that.

> > To be more precise, only hamiltonians at most quadratic in x, p leave
> > coherent states invariant.

> And -- for pure states -- it is precisely these Hamiltonians that
> generate unitary transformations that leave the property of having
> a positive Wigner distribution unaltered. These transformations are
> just linear canonical transformations.

Yes, the quadratic hamiltonians generate the representation of the
metaplectic group - a universal double cover of the symplectic group.

> The pure states with positive
> Wigner distributions include coherent states, squeezed coherent states,
> and (if one allows the term "state" to be abused somewhat) states with
> a definite value of Ux + Vp where U and V are real c-numbers.

Let me just, very gently (dont want to go into wars :-), remark that
squeezing may be rather regarded as a manifestation of a quantum
property. A more or less systematic way of treating squeezing as a
signature of entanglement for finite systems may be found here:
quant-ph/0504005 and Refs. therein.

Best,
jarek

[jarek korbicz]

> > If
> > anybody wants to learn more about how to distinct those states, he may
> > want to take a look at Phys. Rev. Lett. 94, 153601 (2005)
>
> This sounds interesting. If you can give an equivalent Arxiv preprint
> reference that would be appreciated.

Sure, it´s quant-ph/0408029

> In the meantime, allow me to point out that with a different ad-hoc
> assumption -- namely, that one uses symmetrically ordered operators when
> calculating averages -- one finds that the quantum states that "behave
> clasically" are precisely those with positive Wigner distributions.

At a first glance it seemed dissapointing to me that the property of
"being classical" depends on the ordering (we have chosen normal as the
most commonly used), but at the end why there should be just one way of
embedding classical statistics into quantum? Why there should be such
an embedding at all? the most important thing is to receive classical
statistics in the limit \hbar -> 0. I´m prepearing a short paper on
that.

> > To be more precise, only hamiltonians at most quadratic in x, p leave
> > coherent states invariant.

> And -- for pure states -- it is precisely these Hamiltonians that
> generate unitary transformations that leave the property of having
> a positive Wigner distribution unaltered. These transformations are
> just linear canonical transformations.

Yes, the quadratic hamiltonians generate the representation of the
metaplectic group - a universal double cover of the symplectic group.

> The pure states with positive
> Wigner distributions include coherent states, squeezed coherent states,
> and (if one allows the term "state" to be abused somewhat) states with
> a definite value of Ux + Vp where U and V are real c-numbers.

Let me just, very gently (dont want to go into wars :-), remark that
squeezing may be rather regarded as a manifestation of a quantum
property. A more or less systematic way of treating squeezing as a
signature of entanglement for finite systems may be found here:
quant-ph/0504005 and Refs. therein.

Best,
jarek

[p.kinsler@imperial.ac.uk]

C. M. Heard <heard@pobox.com> wrote:
> > Phys. Rev. Lett. 94, 153601 (2005)

> This sounds interesting. If you can give an equivalent Arxiv preprint
> reference that would be appreciated.

quant-ph/0408029

--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/

[p.kinsler@imperial.ac.uk]

C. M. Heard <heard@pobox.com> wrote:
> > Phys. Rev. Lett. 94, 153601 (2005)

> This sounds interesting. If you can give an equivalent Arxiv preprint
> reference that would be appreciated.

quant-ph/0408029

--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/

[p.kinsler@imperial.ac.uk]

C. M. Heard <heard@pobox.com> wrote:
> > Phys. Rev. Lett. 94, 153601 (2005)

> This sounds interesting. If you can give an equivalent Arxiv preprint
> reference that would be appreciated.

quant-ph/0408029

--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/

[p.kinsler@imperial.ac.uk]

C. M. Heard <heard@pobox.com> wrote:
> > Phys. Rev. Lett. 94, 153601 (2005)

> This sounds interesting. If you can give an equivalent Arxiv preprint
> reference that would be appreciated.

quant-ph/0408029

--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/

[p.kinsler@imperial.ac.uk]

C. M. Heard <heard@pobox.com> wrote:
> > Phys. Rev. Lett. 94, 153601 (2005)

> This sounds interesting. If you can give an equivalent Arxiv preprint
> reference that would be appreciated.

quant-ph/0408029

--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/

[p.kinsler@imperial.ac.uk]

C. M. Heard <heard@pobox.com> wrote:
> > Phys. Rev. Lett. 94, 153601 (2005)

> This sounds interesting. If you can give an equivalent Arxiv preprint
> reference that would be appreciated.

quant-ph/0408029

--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/

[p.kinsler@imperial.ac.uk]

C. M. Heard <heard@pobox.com> wrote:
> > Phys. Rev. Lett. 94, 153601 (2005)

> This sounds interesting. If you can give an equivalent Arxiv preprint
> reference that would be appreciated.

quant-ph/0408029

--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/

[p.kinsler@imperial.ac.uk]

C. M. Heard <heard@pobox.com> wrote:
> > Phys. Rev. Lett. 94, 153601 (2005)

> This sounds interesting. If you can give an equivalent Arxiv preprint
> reference that would be appreciated.

quant-ph/0408029

--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/

[p.kinsler@imperial.ac.uk]

C. M. Heard <heard@pobox.com> wrote:
> > Phys. Rev. Lett. 94, 153601 (2005)

> This sounds interesting. If you can give an equivalent Arxiv preprint
> reference that would be appreciated.

quant-ph/0408029

--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/

[Souvik]

himog wrote:
> In the one dimensional Shroedinger picture, one has two Fourier dual
> wavefunctions for a particle, namely Psi(x,t) and Phi(p,t). Can one
> derive these wavefunctions uniquely only given the probability
> distributions Psi*Psi and Phi*Phi? My first guess is "no."

No. You lose the phase information of the particle's wavefunction when
you consider |Phi|^2.

However, one can venture educated guesses by phase-retrieval
algorithms.

-Souvik

[Souvik]

himog wrote:
> In the one dimensional Shroedinger picture, one has two Fourier dual
> wavefunctions for a particle, namely Psi(x,t) and Phi(p,t). Can one
> derive these wavefunctions uniquely only given the probability
> distributions Psi*Psi and Phi*Phi? My first guess is "no."

No. You lose the phase information of the particle's wavefunction when
you consider |Phi|^2.

However, one can venture educated guesses by phase-retrieval
algorithms.

-Souvik

[Souvik]

himog wrote:
> In the one dimensional Shroedinger picture, one has two Fourier dual
> wavefunctions for a particle, namely Psi(x,t) and Phi(p,t). Can one
> derive these wavefunctions uniquely only given the probability
> distributions Psi*Psi and Phi*Phi? My first guess is "no."

No. You lose the phase information of the particle's wavefunction when
you consider |Phi|^2.

However, one can venture educated guesses by phase-retrieval
algorithms.

-Souvik

[Souvik]

himog wrote:
> In the one dimensional Shroedinger picture, one has two Fourier dual
> wavefunctions for a particle, namely Psi(x,t) and Phi(p,t). Can one
> derive these wavefunctions uniquely only given the probability
> distributions Psi*Psi and Phi*Phi? My first guess is "no."

No. You lose the phase information of the particle's wavefunction when
you consider |Phi|^2.

However, one can venture educated guesses by phase-retrieval
algorithms.

-Souvik

[Souvik]

himog wrote:
> In the one dimensional Shroedinger picture, one has two Fourier dual
> wavefunctions for a particle, namely Psi(x,t) and Phi(p,t). Can one
> derive these wavefunctions uniquely only given the probability
> distributions Psi*Psi and Phi*Phi? My first guess is "no."

No. You lose the phase information of the particle's wavefunction when
you consider |Phi|^2.

However, one can venture educated guesses by phase-retrieval
algorithms.

-Souvik

[Souvik]

himog wrote:
> In the one dimensional Shroedinger picture, one has two Fourier dual
> wavefunctions for a particle, namely Psi(x,t) and Phi(p,t). Can one
> derive these wavefunctions uniquely only given the probability
> distributions Psi*Psi and Phi*Phi? My first guess is "no."

No. You lose the phase information of the particle's wavefunction when
you consider |Phi|^2.

However, one can venture educated guesses by phase-retrieval
algorithms.

-Souvik

[Souvik]

himog wrote:
> In the one dimensional Shroedinger picture, one has two Fourier dual
> wavefunctions for a particle, namely Psi(x,t) and Phi(p,t). Can one
> derive these wavefunctions uniquely only given the probability
> distributions Psi*Psi and Phi*Phi? My first guess is "no."

No. You lose the phase information of the particle's wavefunction when
you consider |Phi|^2.

However, one can venture educated guesses by phase-retrieval
algorithms.

-Souvik

[Souvik]

himog wrote:
> In the one dimensional Shroedinger picture, one has two Fourier dual
> wavefunctions for a particle, namely Psi(x,t) and Phi(p,t). Can one
> derive these wavefunctions uniquely only given the probability
> distributions Psi*Psi and Phi*Phi? My first guess is "no."

No. You lose the phase information of the particle's wavefunction when
you consider |Phi|^2.

However, one can venture educated guesses by phase-retrieval
algorithms.

-Souvik

[Souvik]

himog wrote:
> In the one dimensional Shroedinger picture, one has two Fourier dual
> wavefunctions for a particle, namely Psi(x,t) and Phi(p,t). Can one
> derive these wavefunctions uniquely only given the probability
> distributions Psi*Psi and Phi*Phi? My first guess is "no."

No. You lose the phase information of the particle's wavefunction when
you consider |Phi|^2.

However, one can venture educated guesses by phase-retrieval
algorithms.

-Souvik