Superintegrable and scale invariant quantum mechanical systems with position dependent mass

TL;DR

This paper classifies quantum systems with position-dependent mass that are both scale invariant and possess second-order integrals of motion, expanding understanding of their symmetries and integrability.

Contribution

It provides a comprehensive classification of Schroedinger equations with position-dependent mass that are scale invariant and have second order integrals of motion.

Findings

Classification of such quantum systems achieved

Identification of conditions for scale invariance

Insights into symmetries and integrability of these systems

Abstract

Schroedinger equations with position dependent mass which are scale invariant and admit second order integrals of motion are classified.