B\"acklund--Darboux transformations of traslationally shape-invariant potentials

TL;DR

This paper introduces a new framework using Bäcklund--Darboux transformations to incorporate recently discovered translational shape-invariant potentials into the existing classification.

Contribution

It presents a novel approach employing Bäcklund--Darboux transformations to include new shape-invariant potentials not previously classified.

Findings

New translational shape-invariant potentials are integrated into the classification.

The framework offers a systematic way to generate and analyze such potentials.

Potential applications in quantum mechanics and exactly solvable models.

Abstract

Recently, Quesne on the one side and on the other side Bougie, Gangopadhyaya and Mallow, have discovered new translational shape invariant potentials not present in previous classifications. By using ordinary B\"acklund--Darboux transformations we propose a new framework in which such shape invariant potentials can be accommodated.