Vol 3 - Landau, Lifshitz - Quantum mechanics - non-relativistic theory (3ed., 1991) · Problem 45.2

The Quasi-Classical Case

Physics — Landau & Lifshitz · energy-level-two-dimensional-shallow-well

Problem

Determine the energy level in a two-dimensional potential well

U(r)

(where

r

is the polar coordinate in the plane) of small depth; it is assumed that the integral

\displaystyle\int_0^\infty r U\,\mathrm{d}r

converges.