Superselection Rule Results from Schrodinger Equation

  • Thread starter StevieTNZ
  • Start date
  • Tags
    Rules
In summary: By definition, if two states \psi_1,\psi_2 belong to different superselection sectors, then\def\<{\langle}\def\>{\rangle}\<\psi_1|A|\psi_2\> = 0for all observables A. This can be extended to unitaries U = e^{iA} by expanding the exponential.Now consider U(t) = \exp(iHt) and consider \psi_2 at a specific time, say t=0. Then we have0 ~=~ \<\psi_1| U(t) |\psi_2
  • #1
StevieTNZ
1,933
878
From what I've gathered, certain physical states cannot exist in superposition. When applying the Schrodinger equation to a quantum system, do we get the relevant superselection rule results, or will it produce an answer giving two physical states in superposition, when according to the superselection rule cannot occur?
 
Physics news on Phys.org
  • #2
StevieTNZ said:
From what I've gathered, certain physical states cannot exist in superposition. When applying the Schrodinger equation to a quantum system, do we get the relevant superselection rule results, or will it produce an answer giving two physical states in superposition, when according to the superselection rule cannot occur?
It wouldn't be much use to have a superselection rule which applies today, but doesn't apply tomorrow...
 
  • #4
strangerep said:
It wouldn't be much use to have a superselection rule which applies today, but doesn't apply tomorrow...

I don't know what that response has to do with my question...

Demystifier said:
We already have a similar thread:
https://www.physicsforums.com/showthread.php?t=548541

I don't see any answer to my question in that thread. Unless I've overlooked it?
 
  • #5
StevieTNZ said:
strangerep said:
It wouldn't be much use to have a superselection rule which applies today, but doesn't apply tomorrow...
I don't know what that response has to do with my question...

The (time-dependent) Schrodinger equation expresses how a wave function evolves continuously in time.

(If that's still not a relevant answer for you, perhaps you should elaborate your question in more detail?)
 
  • #6
strangerep said:
The (time-dependent) Schrodinger equation expresses how a wave function evolves continuously in time.

(If that's still not a relevant answer for you, perhaps you should elaborate your question in more detail?)

But does the equation take into account superselection rules? Or will it produce superpositions of states that can't occur due to superselection rules?
 
  • #7
StevieTNZ said:
But does the equation take into account superselection rules? Or will it produce superpositions of states that can't occur due to superselection rules?
By definition, if two states [itex]\psi_1,\psi_2[/itex] belong to different superselection sectors, then
[tex]
\def\<{\langle}
\def\>{\rangle}
\<\psi_1|A|\psi_2\> = 0
[/tex]
for all observables [itex]A[/itex]. This can be extended to unitaries [itex]U = e^{iA}[/itex] by expanding the exponential.

Now consider [itex]U(t) = \exp(iHt)[/itex] and consider [itex]\psi_2[/itex] at a specific time, say [itex]t=0[/itex]. Then we have
[tex]
0 ~=~ \<\psi_1| U(t) |\psi_2(0)\> ~=~ \<\psi_1|\psi_2(t)\>
[/tex]
which shows that [itex]\psi_2(t)[/itex] is still orthogonal to [itex]\psi_1[/itex], no matter what superposition of states [itex]\psi_2(0)[/itex] evolves into during the time interval t.
 
  • Like
Likes A. Neumaier

1. What is the superselection rule in relation to the Schrodinger equation?

The superselection rule is a principle in quantum mechanics that states that certain observables, such as energy or angular momentum, are conserved and cannot be changed through unitary transformations. This means that the eigenvalues of these observables remain constant over time, as determined by the Schrodinger equation.

2. How does the Schrodinger equation account for superselection rule?

The Schrodinger equation is a fundamental equation in quantum mechanics that describes the time evolution of a quantum system. It takes into account the superselection rule by incorporating the conserved observables as operators in the equation, which results in their eigenvalues remaining constant over time.

3. Are there any exceptions to the superselection rule in the Schrodinger equation?

Yes, there are exceptions to the superselection rule in certain cases. For example, when a quantum system is in a highly entangled state, the superselection rule may not apply and the conserved observables may change over time. Additionally, in certain non-equilibrium systems, the superselection rule may not hold.

4. How does the concept of superselection rule impact quantum measurements?

The superselection rule has a significant impact on quantum measurements. It ensures that certain observables have well-defined values and that these values are conserved over time. This allows for accurate and consistent measurements of these observables, which is crucial in experimental quantum physics.

5. Can the superselection rule be violated?

No, the superselection rule cannot be violated. It is a fundamental principle in quantum mechanics that is supported by experimental evidence. Any violation of the superselection rule would contradict our current understanding of quantum physics.

Similar threads

  • Quantum Physics
5
Replies
143
Views
5K
  • Quantum Physics
Replies
2
Views
839
  • Quantum Physics
Replies
9
Views
2K
Replies
8
Views
2K
  • Quantum Physics
4
Replies
124
Views
3K
  • Quantum Physics
Replies
17
Views
1K
Replies
26
Views
5K
Replies
3
Views
1K
  • Quantum Physics
Replies
9
Views
2K
Back
Top