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

Abstract

Quantum mechanical systems with position dependent masses (PDM) admitting four and more dimensional symmetry algebras are classified. Namely, all PDM systems are specified which, in addition to their invariance with respect to 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.