Quasiclassical Study of the Quantum Mechanical Two-Coulomb-Centre Problem

Abstract

A recurrent scheme for finding the quasiclassical solutions of the one-dimensional equation got by the separation of variables from the Schrödinger equation in prolate spheroidal coordinates has been elaborated. By means of this scheme, WKB expansion quasiclassical two-Coulomb-centre wave functions at large distances between the fixed positive charges (nuclei) have been constructed for the entire space of the negative particle (electron). Our method provides simple uniform estimates of the eigenfunctions at arbitrary internuclear distances R, R<<1 included. In contrast to the perturbation theory, the interaction need not be very small in the quasiclassical approximation. Its applicability domain is hence wider. That permits analyzing qualitative laws for the behavior and properties of quantum mechanical systems.