Double Shape Invariance of Two-Dimensional Singular Morse Model

TL;DR

This paper discovers a second shape invariance property of a two-dimensional Morse potential, enabling algebraic construction of part of its spectrum despite the lack of conventional separation of variables.

Contribution

It introduces a novel second shape invariance property for the 2D Morse potential, facilitating algebraic spectrum construction from a single state.

Findings

Identified a second shape invariance property of the 2D Morse potential.

Enabled algebraic derivation of part of the spectrum.

Demonstrated the method starting from a specific state.

Abstract

A second shape invariance property of the two-dimensional generalized Morse potential is discovered. Though the potential is not amenable to conventional separation of variables, the above property allows to build purely algebraically part of the spectrum and corresponding wave functions, starting from {\it one} definite state, which can be obtained by the method of $SUSY$-separation of variables, proposed recently.