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

2022/10/30 by Nikitin, A. G.
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2210.16936

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.

Related

• Integrable and superintegrable quantum mechanical systems with position dependent masses invariant with respect to one parametric Lie groups. 1. Systems with cylindric symmetry
• Superintegrable and scale invariant quantum mechanical systems with position dependent mass
• Superintegrable systems with position dependent mass: master symmetry and action-angle methods
• Symmetry algebras for superintegrable systems
• Hamiltonians separable in Cartesian coordinates and third-order integrals of motion