Classical-Limit Quantization of Nonseparable Systems: Multidimensional WKB Perturbation Theory

Abstract

A general dynamical system of N degrees of freedom is considered as a zeroth order separable part plus a nonseparable perturbation, and explicit formulas are derived for the classical-limit approximation to the eigenvalues through second order in the nonseparable interaction. As a numerical example, the first and second order perturbation energies of the helium atom are calculated semiclassically, and agreement with the exact quantum mechanical values is quite reasonable.