behaviour of spin

[ilper@abv.bg]

If i have prepared an electron with a definitive spin projection along
x axis (say up) and I accelerate the electron by an E field would the
spin projection on x axis change according to QM?

[Arkadiusz Jadczyk]

On Thu, 4 May 2006 05:38:54 +0000 (UTC), ilper@abv.bg wrote:

>If i have prepared an electron with a definitive spin projection along
>x axis (say up) and I accelerate the electron by an E field would the
>spin projection on x axis change according to QM?

You probably mean "E field that is constant in time", otherwise it would
have created a magnetic field.

Now, if there is ONLY electric field (in your reference system) and if
we use the Pauli equation, then the time evolution of the state (in this
reference frame) will not affect spin components, so your state will
stay being an eigenstate
of sigma_x. That is, as one can say, spin will still be oriented along
the x axis.

The spin matrices enter Pauli.s equation only through the product
sigma.B, B being the magnetic field.

That is the theory valid in fields that are "not too strong" and for
idealized particles that moving "not too fast" and are "point particles
with no internal structure"

ark
--

Arkadiusz Jadczyk
http://quantumfuture.net/quantum_future/jadpub.htm
--

[ilper@abv.bg]

Thank you very much. This helps a lot.
Just one more thing.
Can I by the use of a constant field E to change the trajectory of the
electron (E perpendicular to electrons trajectory or so) and spin still
to remain the same (up) to my z (not to the electrons trajectory)? I
mean electron will emit photons carring angular momentum!? Or this
doesn't matter to spin?

[Arkadiusz Jadczyk]

On Tue, 9 May 2006 17:34:59 +0000 (UTC), ilper@abv.bg wrote:

>Thank you very much. This helps a lot.
>Just one more thing.
>Can I by the use of a constant field E to change the trajectory of the
>electron (E perpendicular to electrons trajectory or so) and spin still
>to remain the same (up) to my z (not to the electrons trajectory)? I
>mean electron will emit photons carring angular momentum!? Or this
>doesn't matter to spin?

I do not know how to answer this. When you start to consider radiation,
you go beyond quantum mechanics and you move into QFT (Quantum
Electrodynamics). Then you go beyond one-particle quantum mechanics.
You electric field may cause creation-annihilation processes. There will
be a lot of possible effects, and your question is then even not well
phrased. It is necessary to know what kind of an approximation we are
talking about, and I am not well versed in these matters. Perhaps
someone else, with better training in QED, will be able to guide you in
this direction....
--

Arkadiusz Jadczyk
http://quantumfuture.net/quantum_future/jadpub.htm
--

[ilper@abv.bg]

Arkadiusz Jadczyk wrote:
> On Tue, 9 May 2006 17:34:59 +0000 (UTC), ilper@abv.bg wrote:
>
> >Thank you very much. This helps a lot.
> >Just one more thing.
> >Can I by the use of a constant field E to change the trajectory of the
> >electron (E perpendicular to electrons trajectory or so) and spin still
> >to remain the same (up) to my z (not to the electrons trajectory)? I
> >mean electron will emit photons carring angular momentum!? Or this
> >doesn't matter to spin?
>
> I do not know how to answer this. When you start to consider radiation,
> you go beyond quantum mechanics and you move into QFT (Quantum
> Electrodynamics). Then you go beyond one-particle quantum mechanics.
> You electric field may cause creation-annihilation processes. There will
> be a lot of possible effects, and your question is then even not well
> phrased. It is necessary to know what kind of an approximation we are
> talking about, and I am not well versed in these matters. Perhaps
> someone else, with better training in QED, will be able to guide you in
> this direction....
> --
>
> Arkadiusz Jadczyk
> http://quantumfuture.net/quantum_future/jadpub.htm
> --

I thought that your earlier answer will hold true in this case too
(changing of trajectory)
A quote from your letter follows:

Now, if there is ONLY electric field (in your reference system) and if
we use the Pauli equation, then the time evolution of the state (in
this
reference frame) will not affect spin components.

I dont see why this considerations will brake when the E field is
perpendicular, if they hold true when E is colinear. If E is colinear
there will be also accelarations and photons to be emitted by the
electron. Should I then refer to QED for the spin too??