Analytic Independent Particle Model for Molecules

Abstract

Solutions to the Schrödinger equation for an electron in an analytic spheroidal potential are considered. The analysis is carried out in the prolate spheroidal coordinate system resulting in a simple second-order differential equation, which is solved numerically by the Cowell-Numerov method. Computations are presented for models of nitrogen and oxygen molecules. The energy levels can be brought into reasonable accord with experimental Rydberg levels by the adjustment of the two parameters of the spheroidal potential. The results of this study represent an interesting tutorial example of a realistic quantum mechanical problem.