Superintegrable systems in two-dimensional quantum mechanics with third-order Lie symmetries

Mikhail Sheftel (sheftel@gursey.gov.tr)
Feza Gursey Institute
P.O. Box 6, Cengelkoy
81220 Istanbul Turkey

Abstract

We study superintegrable potentials for two-dimensional stationary Schrodinger equation which admit at least one third-order Lie symmetry. A comparison is made with superintegrable systems in classical mechanics possessing cubic integrals of motion.