Semiclassical Approximation with two small parameters

TL;DR

This paper introduces a novel semiclassical quantisation method involving two small parameters, enhancing accuracy for a broad class of potentials by accounting for deviations from ideal cases.

Contribution

It presents a new semiclassical approximation framework with two independent parameters, extending traditional methods to handle more general potential deviations.

Findings

Accuracy estimates for special potential cases

Applicable to a wide class of potentials

Improved semiclassical quantisation method

Abstract

We propose a new variant of the semiclassical quantisation with two independent parameters. The first one is proportional to the Planck constant as usually and the second one is connected with a deviation of the given potential from a very wide and important class of them for which an exact condition can be constructed. The accuracy is estimated for a number of special cases