# Scattering from finite square barrier

1. Apr 16, 2013

### bobred

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

$\frac{A+B}{A-B}=\frac{k_1}{k_2}\frac{C+D}{C-D}=\frac{k^2_1}{k^2_2}$

2. Relevant equations
$A+B=C+D$ and $k_{1}A- k_{1}B = k_{2}C- k_{2}D$

$C e^{i k_{2}L}+D e^{- ik_{2}L} = F e^{i k_{1}L}$ and $k_{2}C e^{ ik_{2}L}- k_{2}D e^{-i k_{2}L} = k_{1}F e^{i k_{1}L}$

$k_2 L=\pi/2$

3. The attempt at a solution
I find

$\frac{A+B}{A-B}=\frac{k_1}{k_2}\frac{C+D}{C-D}$

but cannot seem to find

$\frac{k^2_1}{k^2_2}$

Its probably really simple.
Bob

2. Apr 16, 2013

### 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.