Application of the New Form of the Semiclassical Quantization Condition

TL;DR

This paper explores a new semiclassical quantization condition, extending its applicability beyond specific potentials, and proposes an improved interpolating condition for potential wells with asymptotic infinities, discussing its accuracy.

Contribution

It introduces a novel form of the quantization condition that can be applied more broadly and offers an improved interpolating condition for certain potential wells.

Findings

Enhanced accuracy of quantization conditions for specific potentials

Broader applicability of the new quantization form

Discussion on the conditions' precision and limitations

Abstract

We demonstrate how a certain new form of the quantization condition proposed earlier can be used outside the class of potentials for which this form ensures exact spectra. Taking this form as a base we get an improved interpolating condition for the potential wells with coinciding an + and - infinities asymptotical values. Accuracy of the above conditions is discussed.