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Fourier Transform of a wave function

  1. Sep 8, 2013 #1
    1. The problem statement, all variables and given/known data

    [itex] \psi (x) = Ne^{ \frac{-|x|}{a}+ \frac{ixp_o}{/hbar}}[/itex]

    Compute Fourier transform defined by
    ##\phi (p) = \frac{1}{ \sqrt{2 \pi \hbar}} \int \psi (x) e^{ \frac{-ipx} {\hbar}} dx##

    to obtain ## \phi (x) ##
    2. Relevant equations

    Fourier transform = ##g(x)= \frac {1}{2 \pi} \int f(p) e^{ipx} dx ##

    3. The attempt at a solution

    I tried first solving the integral of ##\phi (p)##

    and I got this hopeless answer of

    ## \frac{N(-a- \frac{i \hbar p - i \hbar p_o}{p_o p})} { \sqrt{2 \pi \hbar}}##

    When I plugged that into the fourier transform, my final answer wound up being some coefficients times ##e ^ \infty##

    This problem has multiple steps and depends on me being able to figure out what the ## \phi (x) ## is


    Help. I don't know what I'm doing wrong?
     
  2. jcsd
  3. Sep 8, 2013 #2

    vela

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    Show your work.
     
  4. Sep 9, 2013 #3

    rude man

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    Why are you bringing up an (incorrect) formula for the Fourier transform when the problem has already defined it for you?

    I can't figure out what the exponent of ψ(x) is however. What does " /hbar " mean?

    Also, the Fourier integral integrates w/r/t x so phi will not be a function of x. So phi(x) is another mystery.
     
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