Matrix Superpotential Linear in Variable Parameter

TL;DR

This paper classifies all irreducible matrix superpotentials with linear variable dependence for shape invariant Schrödinger systems, providing explicit forms across arbitrary dimensions.

Contribution

It offers a comprehensive explicit classification of matrix superpotentials linear in the variable parameter, expanding understanding of shape invariant quantum systems.

Findings

Explicit forms of all inequivalent irreducible matrix superpotentials

Classification across arbitrary matrix dimensions

Enhanced understanding of shape invariant Schrödinger systems

Abstract

The paper presents the classification of matrix valued superpotentials corresponding to shape invariant systems of Schr\"odinger equations. All inequivalent irreducible matrix superpotentials realized by matrices of arbitrary dimension with linear dependence on variable parameter are presented explicitly.