Exactness of Semiclassical Quantization Rule for Broken Supersymmetry

TL;DR

This paper proves that the exactness of a supersymmetry-based semiclassical quantization rule for broken supersymmetry stems from the additive shape invariance of the related potentials, explaining why certain semiclassical methods are exact.

Contribution

It establishes a theoretical proof linking the exactness of semiclassical quantization to shape invariance in supersymmetric quantum mechanics.

Findings

Proves the conjecture that semiclassical quantization is exact for broken supersymmetry.

Shows the connection between shape invariance and quantization exactness.

Provides a theoretical foundation for the observed exactness in specific quantum systems.

Abstract

Semiclassical methods provide important tools for approximating solutions in quantum mechanics. In several cases these methods are intriguingly exact rather than approximate, as has been shown by direct calculations on particular systems. In this paper we prove that the long-conjectured exactness of the supersymmetry-based semiclassical quantization condition for broken supersymmetry is a consequence of the additive shape invariance for the corresponding potentials.