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Homework Help: Quantum Physics A(k) to psi(x)

  1. Sep 10, 2008 #1
    1. The problem statement, all variables and given/known data

    this problem is from (chapter 2 problem 1, gasiorowicz, quantum physics) where I am given
    A(k) = N/(k2+a2) and must calculate psi(x)


    2. Relevant equations

    I am using the equation
    psi(x,t) = integral from - infinity to + infinity A(k) ei(kx-wt) dk

    which when t=0 goes to

    psi(x,t) = integral from - infinity to + infinity A(k) eikx dk

    3. The attempt at a solution

    integral from - infinity to + infinity of
    N/(k2+a2) * eikx dk

    is this a good approach? How can I solve the integral?

    any help would be greatly appreciated

    thank you
     
  2. jcsd
  3. Sep 10, 2008 #2

    nrqed

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    Homework Helper
    Gold Member

    yes it is the right approach.
    just write
    k2 + a2 as (k+ia)(k-ia)
    and then do the integral in the complex k plane, closing above the real k axis so that eikx goes to zero and use the residue theorem
     
  4. Sep 11, 2008 #3
    Thank you so much! would the residue then be e-ax/2ai ?
     
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