Integrable and superintegrable quantum mechanical systems with position dependent masses invariant with respect to one parametric Lie groups. 2. Systems with dilatation and shift symmetries

TL;DR

This paper classifies 27 three-dimensional quantum systems with position-dependent masses that admit specific symmetries and second order integrals of motion, expanding understanding of their integrability and symmetry properties.

Contribution

It provides a complete classification of PDM quantum systems with dilatation or shift symmetries and second order integrals of motion, filling a gap in the understanding of their symmetry structures.

Findings

27 systems explicitly specified

Classification completeness proved

Symmetry properties identified

Abstract

3d quantum mechanical systems with position dependent masses (PDM) admitting at least one second order integral of motion and symmetries with respect to dilatation or shift transformations are classified. Twenty-seven such systems are specified and the completeness of the classification results is proved.