Principles of Quantum Mechanics · Problem 19.5

Scattering Theory — R. Shankar

Physics — Quantum Mechanics · partial-wave-analysis

Problem

Find the

s

-wave (

l = 0

) phase shift

\delta_0

for scattering from a hard sphere of radius

a

(i.e.,

V(r) = \infty

for

r < a

and

V(r) = 0

for

r > a

). Show that

\delta_0 = -ka

. Compute the total cross section in the low-energy limit and compare with the classical result.