New Two-Dimensional Quantum Models Partially Solvable by Supersymmetrical Approach

TL;DR

This paper introduces new two-dimensional quantum models solvable by supersymmetry, deriving explicit spectra and eigenfunctions for generalized P"oschl-Teller potentials using advanced SUSY techniques.

Contribution

It develops a novel method for solving 2D SUSY quantum models, providing explicit solutions and analyzing higher-order intertwining relations.

Findings

Derived new 2D shape-invariant potentials

Obtained explicit energy spectra and eigenfunctions

Explored higher-order intertwining relations

Abstract

New solutions for second-order intertwining relations in two-dimensional SUSY QM are found via the repeated use of the first order supersymmetrical transformations with intermediate constant unitary rotation. Potentials obtained by this method - two-dimensional generalized P\"oschl-Teller potentials - appear to be shape-invariant. The recently proposed method of $SUSY-$separation of variables is implemented to obtain a part of their spectra, including the ground state. Explicit expressions for energy eigenvalues and corresponding normalizable eigenfunctions are given in analytic form. Intertwining relations of higher orders are discussed.