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Scattering from finite square barrier

  1. Apr 16, 2013 #1
    1. The problem statement, all variables and given/known data
    Use the boundary conditions to show that

    [itex]\frac{A+B}{A-B}=\frac{k_1}{k_2}\frac{C+D}{C-D}=\frac{k^2_1}{k^2_2}[/itex]

    2. Relevant equations
    [itex]A+B=C+D[/itex] and [itex]k_{1}A- k_{1}B = k_{2}C- k_{2}D[/itex]

    [itex]C e^{i k_{2}L}+D e^{- ik_{2}L} = F e^{i k_{1}L}[/itex] and [itex]k_{2}C e^{ ik_{2}L}- k_{2}D e^{-i k_{2}L} = k_{1}F e^{i k_{1}L}[/itex]

    [itex]k_2 L=\pi/2[/itex]

    3. The attempt at a solution
    I find

    [itex]\frac{A+B}{A-B}=\frac{k_1}{k_2}\frac{C+D}{C-D}[/itex]

    but cannot seem to find

    [itex]\frac{k^2_1}{k^2_2}[/itex]

    Its probably really simple.
    Bob
     
  2. jcsd
  3. Apr 16, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    k_1(A-B)=k_2(C-D)
    Use this to replace (C-D) in the last equation, and replace (C+D) by (A+B) in the numerator.
     
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