On the Wave Equation with Small Quantum Numbers

Publisher Website
Google Scholar
Abstract
The determination of the Eigenwerte, and the normalization of the Eigenfunktionen of the one-dimensional wave equation, with a potential energy that has a single minimum, is customarily based on the use of the so-called phase integral and W.K.B. formulas. These formulas are asymptotic in character. As they have usually been applied, they accordingly lead to conclusions which can be regarded as established only when the respective quantum numbers are sufficiently large. This restriction has been both unfortunate and puzzling. For on the one hand, the cases of small or moderate quantum numbers are often peculiarly interesting while, on the other hand, the phase integral formulas have been found by trial, at least in a variety of simple cases, to give surprisingly good results even in the lower quantum number range.

This publication has 2 references indexed in Scilit: