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Time dependent scattering theory - cross section

  1. Nov 10, 2014 #1

    tom.stoer

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    I am looking for a realistic explanation of the double-slit experiment in terms of wave packets (instead of stationary waves). First of all this results in using the scattering cross section, i.e. the probability current (not the density). Then, I guess, there is a kind of time average. So one should end up with something like

    [tex]j_\text{scatt}(x,t) \sim \text{Im}\psi^\ast\nabla\psi[/tex]

    calculated for a scattered wave packet

    [tex]|\psi,t\rangle = U(t,t_0)\,|\psi,t_0\rangle[/tex]

    and an integration like

    [tex]N(\Omega) \sim \int_{-T}^{+T}dt\,\int_\Omega d\Omega \, j_\text{scatt}(x,t)[/tex]

    to calculate the number of particles N detected in Omega on a spherical screen.

    Is there a rigorous derivation of such an expression for wave packets using e.g. time-dependent scattering theory?
     
    Last edited: Nov 10, 2014
  2. jcsd
  3. Nov 15, 2014 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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