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Homework Help: A Problem with Lippmann-Schwinger Equation

  1. Oct 14, 2008 #1
    I am doing Problem 3.1 from Quantum Theory of Fields by Steven Weinberg regaring the Lippmann-Schwinger Equation. The problem states,

    Given a separable interaction,

    [tex]\langle \alpha_{0}|V|\beta_{0}\rangle=g u_{\alpha}u_{\beta}^{*}[/tex]

    where [tex]g[/tex] is a real coupling constant, and [tex]u_{\alpha}[/tex] is a set of complex quantities with


    Use the Lippmann-Schwinger equation to find explicit solutions for the 'in' and 'out' state and the S-matrix.

    I believe I have solved this to the second order in [tex]g[/tex], but I'm not sure if it is correct since there are no solutions. What I found puzzling is that my S-matrix has 0 contribution for the first order [tex]g[/tex]. Is this suppose to happen? I do not want to show the working since it is too much mathematics. I am just wondering if there are anyone who has done similar problems.

    Any comment is appreciated!
    Last edited: Oct 14, 2008
  2. jcsd
  3. Apr 5, 2017 #2
    I am facing a similar problem too. I solved it up to 2nd order, and there was no contribution to the S-matrix at [tex]O(g)[/tex] Also, I was wondering if there are non-approximate exact solutions. Did you find anything else?
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