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Expectation values in momentum/position space?

  1. May 10, 2004 #1
    I'm currently, yet again, left clueless by a problem.

    See: the actual equations here

    Ok, so they give the Psi(x) in position space, and the first question is to give the corresponding, normalized wave equation in momentum space.

    You do a fourier transform, no?

    Psi(p)=Int ((1/sqrt2pi) Psi(x) (e^ipx/hbar) dx


    no?

    From that, I get Psi(p)=(2hbar/(p sqrt2pi)) sin (pa/hbar)


    or....?


    After that, I tried to get the expectation value, <p>, but with poor results. Integrate Psi* Psi p dp, yeah? What I get is 4hbar^2/(2pi p^2) [ln|p| sin^2(pa/hbar)]


    Now, I know this has to be wrong, but I have no idea what I'm doing to screw it up.

    I tried to do <p^2> and <x> and it just gets worse, and messier. WHAT AM I DOING WRONG??


    Pleease help. Thank you :)




    edit: I think I've got it! Well, at least part of it. I've gotten my expectation values for p and x to be zero, and I think my x^2 and p^2 are wrong, but... I can't think of anything else... so, it's staying right now with

    <p^2>= (2hbarp*sinpa)/pi

    <x^2>= A^2 (2a^3/3)

    Working on the rest, still... but coming a bit further?
     
    Last edited: May 10, 2004
  2. jcsd
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