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Expectation value of a dynamical variable problem.

  1. Feb 23, 2013 #1
    1. The problem statement, all variables and given/known data
    Why does the extra phase factor cancel out? Is it because you are multiplying the wave-function with the extra phase factor by its conjugate and if so, why should it matter that the extra phase factor is independent of x?

    All relevant information, the solution and equation referred to in the solution is given below:

    Prob18.jpg

    2. Relevant equations

    Given in picture


    3. The attempt at a solution

    See problem statement
     
  2. jcsd
  3. Feb 23, 2013 #2

    Dick

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    Yes, the phase get multiplied by its conjugate. If the phase had had an x dependence then when the operator Q (which could contain d/dx) acts on ψ it could also change the phase factor.
     
  4. Feb 23, 2013 #3
    Oh I see :) Because the phase factor is independent of x it acts as a constant on ψ so taking the derivative of one of the ψ's wouldn't affect the value of the phase factor, but if it was dependent of x one would need to use the product rule to take the partial of one of the psi's.
     
  5. Feb 23, 2013 #4

    Dick

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    Right! The phase has to commute with the operator Q if it's not going to change expectation values.
     
  6. Feb 23, 2013 #5
    Cool, thanks :D
     
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