Principles of Quantum Mechanics · Problem 19.22

Scattering Theory — R. Shankar

Physics — Quantum Mechanics · born-approximation

Problem

Determine the condition for the validity of the Born approximation for the Gaussian potential

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

at: (a) Low energies (

ka \ll 1

). (b) High energies (

ka \gg 1