Superintegrability, isochronicity, and quantum harmonic behavior

Simon Gravel

Published 2003-10-03Version 1

We discuss the properties of superintegrable Hamiltonian systems, in particular those that admit separation of variables in cartesian coordinates. We show that the superintegrability of such potentials is equivalent to the isochronicity of the separated potentials. We use this fact to get a new insight into an old question about the relation between quantum and classical harmonic behavior.