General Solution of the Two-Dimensional Intertwining Relations for Supercharges with Hyperbolic (Lorentz) Metrics

TL;DR

This paper derives the general solution for two-dimensional supersymmetric intertwining relations with hyperbolic supercharges, explicitly constructing new potentials that extend previous known solutions in quantum mechanics.

Contribution

It provides the first comprehensive general solution for hyperbolic intertwining relations in 2D supersymmetric quantum mechanics, including novel potentials not previously identified.

Findings

Derived the general solution for hyperbolic supercharge intertwining relations.

Constructed explicit forms of new two-dimensional potentials.

Identified previously unknown potentials within the framework.

Abstract

The supersymmetrical intertwining relations are the most productive part of the supersymmetrical method in two-dimensional Quantum Mechanics. Most interesting are relations with hyperbolic form of derivatives in supercharges. So far, several explicit solutions were found, and they provide nontrivial two-dimensional potentials which were further studied by means of supersymmetrical methods. In the present paper the general solution of intertwining relations with hyperbolic structure of supercharges is obtained. The corresponding potentials are built explicitly, and it is evident that some of them were not known before now.