Is the Lowest Order Supersymmetric WKB Approximation Exact for All Shape Invariant Potentials ?

TL;DR

This paper investigates the accuracy of the lowest order supersymmetric WKB approximation for shape invariant potentials, revealing it is not universally exact as previously thought, especially for newly discovered classes.

Contribution

It demonstrates that the lowest order supersymmetric WKB approximation is not exact for a new class of shape invariant potentials, challenging prior assumptions.

Findings

The approximation fails for certain new shape invariant potentials.

The paper analyzes reasons for the breakdown of the approximation.

It extends understanding of the limitations of supersymmetric WKB methods.

Abstract

It has previously been proved that the lowest order supersymmetric WKB approximation reproduces the exact bound state spectrum of shape invariant potentials. We show that this is not true for a new, recently discovered class of shape invariant potentials and analyse the reasons underlying this breakdown of the usual proof.