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

Abstract

Quantum mechanical systems with position dependent masses (PDMs) admitting two parametric Lie symmetry groups are classified. Namely, all PDM systems are specified which, in addition to their invariance w.r.t. a two parametric Lie group, admit at least one second order integral of motion. The presented classification is partially extended to the more generic systems which do not accept any Lie group.