Two-dimensional Schr\"odinger Hamiltonians with Effective Mass in SUSY Approach

TL;DR

This paper develops a general framework for solving two-dimensional Schrödinger Hamiltonians with position-dependent mass using supersymmetric (SUSY) methods, including first and second order intertwining relations, and explores their properties.

Contribution

It introduces a comprehensive solution for SUSY intertwining relations with position-dependent mass, including separation of variables and higher-order generalizations.

Findings

Constructed general solutions using four arbitrary functions

Demonstrated separation of variables for the potentials

Analyzed properties of second order intertwining operators

Abstract

The general solution of SUSY intertwining relations of first order for two-dimensional Schr\"odinger operators with position-dependent (effective) mass is built in terms of four arbitrary functions. The procedure of separation of variables for the constructed potentials is demonstrated in general form. The generalization for intertwining of second order is also considered. The general solution for a particular form of intertwining operator is found, its properties - symmetry, irreducibility, separation of variables - are investigated.