General solution of the two-dimensional intertwining relations for supercharges with hyperbolic (Lorentz) metrics

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 Letter 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.