Superintegrable quantum mechanical systems with position dependent masses invariant with respect to three parametric Lie groups

TL;DR

This paper classifies quantum systems with position-dependent masses that are invariant under certain Lie groups and possess additional symmetries, extending previous classifications to more general cases.

Contribution

It provides a comprehensive classification of PDM quantum systems with three-parameter Lie group invariance and extends results to systems with fewer symmetries.

Findings

Classified all PDM systems with three-parameter Lie group invariance.

Extended classification to systems with fewer symmetry parameters.

Identified systems admitting second order integrals of motion.

Abstract

Quantum mechanical systems with position dependent masses (PDM) admitting for and more dimensional symmetry algebras are classified. Namely, all PDM systems are specified which, in addition to their invariance w.r.t. a three parametric Lie group, admit at least one second order integral of motion. The presented classification is partially extended to the more generic systems which admit one or two parametric Lie groups.