Principles of Quantum Mechanics · Problem 19.8

Scattering Theory — R. Shankar

Physics — Quantum Mechanics · born-approximation

Problem

Determine the Born approximation to the total cross section for the potential

V(r) = V_0 e^{-r^2/a^2}

. You may use the result that the three-dimensional Fourier transform of

e^{-r^2/a^2}

\pi^{3/2} a^3 e^{-q^2 a^2/4}