Introduction to Quantum Mechanics · Problem 10.20

Scattering — David J. Griffiths

Physics — Quantum Mechanics · born-approximation-gaussian-potential

Problem

Use the Born approximation to determine the total cross-section for scattering from a gaussian potential

V(\mathbf{r}) = V_0 e^{-\mu r^2/a^2}.

Express your answer in terms of the constants

V_0

a

, and

m

(the mass of the incident particle), and

k \equiv \sqrt{2mE}/\hbar

, where

E

is the incident energy.