Algebraic Shape Invariant Models

TL;DR

This paper introduces an algebraic framework for shape invariant Hamiltonians inspired by supersymmetric quantum mechanics, utilizing nonlinear Lie algebra generalizations to extend previous models and encompass a broader class of potentials.

Contribution

It develops a new algebraic approach for shape invariance using nonlinear Lie algebras, generalizing existing models to include more potential types.

Findings

Extended algebraic framework for shape invariant Hamiltonians.

Unified treatment of translational shape invariance with potential algebra.

Broadened the class of solvable potentials beyond Natanzon type.

Abstract

Motivated by the shape invariance condition in supersymmetric quantum mechanics, we develop an algebraic framework for shape invariant Hamiltonians with a general change of parameters. This approach involves nonlinear generalizations of Lie algebras. Our work extends previous results showing the equivalence of shape invariant potentials involving translational change of parameters with standard $SO(2,1)$ potential algebra for Natanzon type potentials.