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

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.