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Homework Help: Question about quantum

  1. Nov 5, 2007 #1
    Sorry... my message got posted by mistake before I started typing. Here is what I was going to say:

    I'm having a problem just understanding something from my quantum book. They're deriving something to do with a wave packet with the Schrodinger equation, and they have the equation of a wave packet at time t = 0:

    [tex] \psi(x,0) = \int_{- \infty}^{+ \infty} dk A(k) e^{i(kx) [/tex]

    where [tex] A(k) = e^{- \alpha (k - k_o)^2 / 2} [/tex]

    They change variables to [tex]q' = k - k_o [/tex] and then they get

    [tex] \psi(x,0) = e^{i k_o x} e^{- x^2 / {2 \alpha}} \int_{- \infty}^{+ \infty} dq' e^{- \alpha {q'}^2 / 2} [/tex]

    I don't understand how they got that (specifically, the [tex] e^{-x^2 / {2 \alpha}} [/tex] term).
     
    Last edited: Nov 5, 2007
  2. jcsd
  3. Nov 5, 2007 #2

    Dick

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    They did the substitution and then completed the square in q' in the integral and brought the non-square stuff outside the integral. Finally they shifted q'->q'-ix/alpha.
     
    Last edited: Nov 5, 2007
  4. Nov 6, 2007 #3
    Thanks so much for your help =) =) =) I understand it now.
     
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