Broken Supersymmetric Shape Invariant Systems and Their Potential Algebras

TL;DR

This paper introduces new methods to solve quantum systems with broken supersymmetry, where traditional techniques fail due to the absence of zero energy states, by developing a two-step shape invariance and potential algebra approach.

Contribution

It presents novel two-step shape invariance and potential algebra methods specifically designed for broken supersymmetry systems, expanding solvable models in quantum mechanics.

Findings

Successfully applied the methods to specific broken supersymmetry potentials

Derived explicit energy spectra for previously intractable systems

Established a group theoretic framework for these potentials

Abstract

Although eigenspectra of one dimensional shape invariant potentials with unbroken supersymmetry are easily obtained, this procedure is not applicable when the parameters in these potentials correspond to broken supersymmetry, since there is no zero energy eigenstate. We describe a novel two-step shape invariance approach as well as a group theoretic potential algebra approach for solving such broken supersymmetry problems.