Shape invariance in prepotential approach to exactly solvable models

TL;DR

This paper demonstrates that within the prepotential approach to quantum mechanics, the shape invariance condition necessary for exact solvability is inherently satisfied, eliminating the need for its separate assumption.

Contribution

The authors show that shape invariance naturally arises in the prepotential approach, simplifying the classification of exactly solvable quantum models.

Findings

Shape invariance is automatically satisfied in the prepotential approach.

Elimination of the need for additional shape invariance assumptions.

Simplifies the classification of exactly solvable models.

Abstract

In supersymmetric quantum mechanics, exact-solvability of one-dimensional quantum systems can be classified only with an additional assumption of integrability, the so-called shape invariance condition. In this paper we show that in the prepotential approach we proposed previously, shape invariance is automatically satisfied and needs not be assumed.