New Basic Form of the Semiclassical Quantization Condition

TL;DR

This paper proposes a modified semiclassical quantization condition derived from a power expansion in the squared Planck constant, enabling a new perturbation theory independent of the Planck constant.

Contribution

It introduces a novel modification of the semiclassical quantization condition based on power expansion, facilitating a new kind of perturbation theory not linked to the Planck constant.

Findings

Deviation from exact spectra correlates with potential deviations from supersymmetry.

The method allows development of perturbation theory independent of the Planck constant.

Potential for improved spectral approximations in quantum systems.

Abstract

A certain modification of the semiclassical quantization condition based on the summarization of the known power expansion in the squared Planck constant is proposed. Corresponding deviation from exact spectra arises only together with the deviation of the studied potential from the supersymmetric one so that on the base of the presented method a new kind of the perturbation theory not connected with the Planck constant may be developed