Generalized Langer Correction and the Exactness of WKB for all Conventional Potentials

TL;DR

This paper demonstrates that a generalized Langer correction, derived via supersymmetric quantum mechanics, ensures the exactness of the WKB quantization condition for all conventional translationally shape invariant potentials, linking it to SWKB exactness.

Contribution

It introduces a generalized Langer correction that guarantees WKB exactness for all conventional potentials, extending previous results.

Findings

The generalized Langer correction yields exact WKB quantization.

The correction is connected to the proven exactness of SWKB.

It applies to all conventional translationally shape invariant potentials.

Abstract

In this paper we investigate the exactness of the WKB quantization condition for translationally shape invariant systems. In particular, using the formalism of supersymmetric quantum mechanics, we generalize the Langer correction and show that it generates the exact quantization condition for all conventional potentials. We also prove that this correction is related to the previously proven exactness of SWKB for these potentials.