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Inelastic scattering on a two level atom

  1. Jan 12, 2016 #1
    1. The problem statement, all variables and given/known data
    Consider a scattering problem that is described by the Hamiltonian p%5E2%7D%7B2M%7D%20-%20%5Cfrac%7Bh%7D%7B2%7D%20%5Csigma_z%20+%20u%20%5Csigma_x%20%5Cdelta%28x%29.gif .
    The target is prepared in the lower level. The kinetic energy of the incident particle is Ev. Find the transmission as a function of energy.

    2. Relevant equations
    p%5E2%7D%7B2M%7D%20-%20%5Cfrac%7Bh%7D%7B2%7D%20%5Csigma_z%20+%20u%20%5Csigma_x%20%5Cdelta%28x%29.gif .

    3. The attempt at a solution
    I tried going at this in a straight forward way and defining 2 wave functions for each state and using continuity and discontinuity conditions on x=0 (written in the photo). But from that at the end, using T=|t0|2+|t1|2
    and R=|r0|2+|r1|2 and plugging it on R+T=1, I get a wrong answer which can results in R+T=1 only when k0=k1.
    I think maybe I have a fundamental problem in here but I can seem to pinpoint on it. Thanks
     

    Attached Files:

  2. jcsd
  3. Jan 17, 2016 #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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