The Supersymmetric WKB Formalism is Not Exact for All Additive Shape Invariant Potentials

TL;DR

This paper demonstrates that the supersymmetric WKB (SWKB) method, previously believed to be exact for all additive shape invariant potentials, is not universally accurate by providing a counterexample.

Contribution

The paper presents a specific additive shape invariant potential where the SWKB method fails, challenging the prior assumption of its universal exactness.

Findings

SWKB is not exact for all additive shape invariant potentials

A concrete counterexample of failure is provided

Questions the universality of SWKB's exactness in supersymmetric quantum mechanics

Abstract

Following the verification of the conjecture made by Comtet, Bandrauk and Campbell that the supersymmetry-inspired semiclassical method known as SWKB is exact for the conventional additive shape invariant potentials, it was widely believed that SWKB yields exact results for all additive shape invariant potentials. In this paper we present a concrete example of an additive shape invariant potential for which the SWKB method fails to produce exact results.