Superintegrable systems with third order integrals in classical and quantum mechanics Simon Gravel (graves@magellan.umontreal.ca)
Abstract We will discuss the coexistence of a third order integral of motion with a first or second order one, in 2 dimensional quantum and classical mechanics. We have found explicitely all potentials that admit first and third order integrals, and all their integrals. Quantum superintegrable systems are found that have no classical analog, i.e. the potentials are proportional to hbar^2 so they vanish in the classical limit. |