Ladder operators for subtle hidden shape invariant potentials

TL;DR

This paper constructs ladder operators for certain exactly solvable quantum potentials with hidden shape invariance using supersymmetric quantum mechanics superalgebra.

Contribution

It introduces a method to find ladder operators for potentials with subtle hidden shape invariance, expanding the class of solvable models.

Findings

Ladder operators can be constructed for potentials with hidden shape invariance.

Supersymmetric quantum mechanics superalgebra facilitates this construction.

The approach applies to specific exactly solvable potentials.

Abstract

Ladder operators can be constructed for all potentials that present the integrability condition known as shape invariance, satisfied by most of the exactly solvable potentials. Using the superalgebra of supersymmetric quantum mechanics we construct the ladder operators for two exactly solvable potentials that present a subtle hidden shape invariance.