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Superselection Rules

  1. Jan 3, 2012 #1
    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?
     
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  3. Jan 4, 2012 #2

    strangerep

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    It wouldn't be much use to have a superselection rule which applies today, but doesn't apply tomorrow...
     
  4. Jan 4, 2012 #3

    Demystifier

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  5. Jan 4, 2012 #4
    I don't know what that response has to do with my question.....

    I don't see any answer to my question in that thread. Unless I've overlooked it?
     
  6. Jan 4, 2012 #5

    strangerep

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    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?)
     
  7. Jan 4, 2012 #6
    But does the equation take into account superselection rules? Or will it produce superpositions of states that can't occur due to superselection rules?
     
  8. Jan 5, 2012 #7

    strangerep

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    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.
     
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