Principles of Quantum Mechanics · Problem 19.21

Scattering Theory — R. Shankar

Physics — Quantum Mechanics · scattering-theory-general

Problem

Consider scattering by a

\delta

-function shell potential:

V(r) = \alpha \delta(r - a)

. (a) Find the phase shifts

\delta_l

for all

l

. (b) Find the total cross section in the low-energy limit (

ka \ll 1

), keeping only

l = 0

. (c) Show that when

2mka\alpha/\hbar^2 \to -1

there is a resonance in the

s

-wave.