Potential algebra approach to position dependent mass Schroedinger equation

TL;DR

This paper demonstrates that for certain position-dependent mass Schrödinger equations, shape invariance corresponds to a potential symmetry algebra, with explicit algebra realizations provided for some shape invariant potentials.

Contribution

It establishes the equivalence between shape invariance and potential symmetry algebra in position-dependent mass Schrödinger equations and constructs explicit algebra realizations.

Findings

Shape invariance is equivalent to potential symmetry algebra.

Explicit algebra realizations are obtained for specific shape invariant potentials.

The approach provides a new algebraic perspective on position-dependent mass quantum systems.

Abstract

It is shown that for a class of position dependent mass Schroedinger equation the shape invariance condition is equivalent to a potential symmetry algebra. Explicit realization of such algebras have been obtained for some shape invariant potentials.