# Scattering problem

1. Jan 3, 2008

### ehrenfest

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

$V=A\delta(z)$ for $-a \leq x \leq a$ and $-a \leq y \leq a$

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:
$$4\left(\frac{Am}{K_x K_y \pi \hbar^2}\right)^2\sin^2(K_y a)\sin^2(K_x a)$$
and I don't even see how that is well-defined when a goes to infinity.