The generalized zero-mode supersymmetry scheme and the confluent algorithm

TL;DR

This paper explores a generalized supersymmetry framework in quantum mechanics, connecting recent mathematical approaches with confluent supersymmetric quantum mechanics, and extends the method to Dirac and Fokker-Planck equations.

Contribution

It introduces a generalized scheme for supersymmetry in quantum mechanics and demonstrates its application to Dirac and Fokker-Planck equations, expanding the scope of previous methods.

Findings

Established relationship between recent supersymmetry approaches and confluent SUSY

Proposed immediate generalizations of the existing SUSY framework

Applied the generalized scheme to Dirac and Fokker-Planck equations

Abstract

We show the relationship between the mathematical framework used in recent papers by H.C. Rosu, S.C. Mancas and P. Chen (2014) and the second-order confluent supersymmetric quantum mechanics. In addition, we point out several immediate generalizations of the approach taken in the latter references. Furthermore, it is shown how to apply the generalized scheme to the Dirac and to the Fokker-Planck equation.