Superintegrable and shape invariant systems with position dependent mass

A. G. Nikitin

Published 2014-12-13Version 1

Second order integrals of motion for 3d quantum mechanical systems with position dependent masses (PDM) are classified. Namely, all PDM systems are specified which, in addition to their rotation invariance, admit at least one second order integral of motion. All such systems appear to be also shape invariant and exactly solvable. Among them are $3d$ PDM analogues of isotropic oscillator, Coulomb, Eckart and trigonometric Rosen-Morse systems.