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W is real valued?

  1. Apr 13, 2007 #1
    1. The problem statement, all variables and given/known data
    The question is in the post below.

    Show the equation W posted is real valued.

    3. The attempt at a solution
    The idea is to show that W conjugate = W but there is a complex exponential in W which makes things tricky?
    Last edited: Apr 13, 2007
  2. jcsd
  3. Apr 13, 2007 #2


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    You have posted a link to a restricted web-site.
  4. Apr 13, 2007 #3
    Okay. I have put the equation up in the document. Show W is real valued.

    Attached Files:

  5. Apr 13, 2007 #4
    Is it because psi conjugated produces a negative in the y value so y has only an imaginary component. mod spi sqaured is real. since y has a factor or i, it will cancel with the i already apparent in the exponential. So everything in the integral is positive hence W is positive.
  6. Apr 13, 2007 #5


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    Yes. The imaginary part of the integrand is an odd function ([itex]e^{iy}= cos(y)+ i sin(y)[/itex] and sin is odd) so its integral over a region symmetric about 0 ([itex]-\infty[/itex] to [itex]\infty[/itex] is 0.
  7. Apr 13, 2007 #6
    That is very neat. But is my long explanation also correct? Although in my explantion, I said that y is purely imaginary. Is that correct would sin(y) make sense then?

    In that integral y is claimed to be the integration variable but how does that make sense? Why do you need an integration variable? why not integrate wrt p or x?

    This means y can't be complex valued which raises the question why are the arguments in psi have plus and minus y/2 for non conjugate and conjugate psi.
    Last edited: Apr 13, 2007
  8. Apr 13, 2007 #7
    [itex] y [/itex] is a dummy variable. Imagine if you had a function:

    [tex] f(x) = \sum_{n=1}^x 1 [/tex]

    The integral is no different, [itex] y [/itex] is used to "increment" (so to speak), just as [itex] n [/itex] is.
  9. Apr 13, 2007 #8
    Right, W is a function of x and p and the integral has nothing to do with x or p, it is there to evaluate a number with constants x and p.
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