Quantum, classical symmetries, and action-angle variables by factorization of superintegrable systems

Abstract

The purpose of this work is to present a method based on the factorizations used in one-dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this procedure to the harmonic oscillator and Kepler–Coulomb systems to show the differences with other more standard approaches.We describe in detail the basic ingredients to make explicit the parallelism of classical and quantum treatments. One of the most interesting results is the finding of action-angle variables as a natural component of the classical symmetries within this formalism.