SWKB and proper quantization conditions for translationally shape invariant potentials

TL;DR

This paper demonstrates that the exact quantization rule for translationally shape invariant potentials aligns with the supersymmetric JWKB condition and derives their energy levels.

Contribution

It establishes the equivalence between the Ma and Xu quantization rule and the supersymmetric JWKB condition for specific potentials.

Findings

Quantization rule is equivalent to supersymmetric JWKB.

Energy levels for classified potentials are derived.

Provides a unified understanding of quantization conditions.

Abstract

Using a recently proposed classification for the primary translationally shape invariant potentials, we show that the exact quantization rule formulated by Ma and Xu is equivalent to the supersymmetric JWKB quantization condition. The energy levels for the two considered categories of shaped invariant potentials are also derived.