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Scattering problem

  1. Jan 3, 2008 #1
    1. The problem statement, all variables and given/known data
    A particle with mass m scatters off of the potential

    [itex]V=A\delta(z)[/itex] for [itex]-a \leq x \leq a[/itex] and [itex]-a \leq y \leq a[/itex]

    V= 0 otherwise

    Find the differential scattering cross-section using the Born approximation and show that in the limit where a goes to infinity the resulting differential cross-section corresponds to only two possible results: either the particle will pass through without any scattering or else it will scatter with angle of incidence equal to angle of reflection.
    2. Relevant equations

    3. The attempt at a solution
    So, I need to prove that K_x=K_y=0 where K is the momentum transfer.
    I got a differential cross-section of:
    [tex] 4\left(\frac{Am}{K_x K_y \pi \hbar^2}\right)^2\sin^2(K_y a)\sin^2(K_x a) [/tex]
    and I don't even see how that is well-defined when a goes to infinity.
  2. jcsd
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