Supersymmetric Construction of three-dimensional isospectral systems

TL;DR

This paper develops methods to construct three-dimensional isospectral quantum systems using supersymmetric quantum mechanics, revealing trivial cases with first-order supercharges and nontrivial systems with second-order supercharges.

Contribution

It introduces a supersymmetric framework for creating nontrivial three-dimensional isospectral systems, extending previous one-dimensional results.

Findings

First-order supercharges lead to trivial generalizations.

Second-order supercharges produce nontrivial three-dimensional systems.

The approach broadens the understanding of isospectral quantum systems.

Abstract

Three-dimensional isospectral systems are constructed using the framework of supersymmetric quantum mechanics. In case the supercharge of first order in momentum is used, it is proved that the constructed systems reduce to a trivial generalization of one-dimensional systems. In case the second order supercharge is used, nontrivial three-dimensional isospectral systems are constructed.