Anatoly Nikitin (Institute of Mathematics, Kyiv)

Superintegrable and shape invariant systems with position dependent mass

Abstract:
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 shape invariant and exactly solvable. Moreover, some of them possess the property of double shape invariance and can be solved using two different superpotentials. A simple algorithm for calculating the discrete spectrum and the corresponding state vectors for the considered PDM systems is presented and applied to some of the found systems.

This talk is based on the paper J. Phys. A: Math. Theor. 48 (2015), 335201, 24 pp., arXiv:1412.4232.