1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    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 ?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Quantum Physics A(k) to psi(x)
  1. Calculate |Psi(x,t)|^2 (Replies: 2)

Loading...