- #1
ehrenfest
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Homework Statement
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.
Homework Equations
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.