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Quantum Physics: Fourier transform of a function

  1. Sep 18, 2010 #1
    1. The problem statement, all variables and given/known data
    Let [tex]\phi (k)[/tex] be the Fourier transform of the function [tex]\psi (x)[/tex]. Determine the Fourier transform of [tex]e^{iax} \psi (x)[/tex] and discuss the physical interpretation of this result.


    2. Relevant equations
    (1) [tex]\tilde{f} (k) = \frac{1}{\sqrt{2 \pi}} \int{f (x) e^{-ikx} dx}[/tex]
    (2) [tex]\psi (x,0)=\int{\phi(k)e^{ikx}dk}[/tex] (might be needed)


    3. The attempt at a solution
    We know that: [tex]\phi (k) = \tilde{\psi} (x) = \frac{1}{\sqrt{2 \pi}} \int{\psi (x) e^{-ikx} dx}[/tex] (eq. 1)

    I'll let [tex]\tilde{\phi_2} (k)[/tex] be the Fourier transform of [tex]e^{iax} \psi (x)[/tex]

    [tex]\tilde{\phi_2} (k) = \frac{1}{\sqrt{2 \pi}} \int{\psi (x) e^{iax} e^{-ikx} dx} = \frac{e^{a/k}}{\sqrt{2 \pi}} \int{\psi (x) dx}[/tex]

    Can I do anything more? How's the result interesting?
     
    Last edited: Sep 18, 2010
  2. jcsd
  3. Sep 19, 2010 #2

    vela

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    You made an algebraic error: eae-b ≠ ea/b. Fix that and try again.
     
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