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

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 have described 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 sysmmetries within this formalism.Comment: 21 pages, 3 figure

SUSY partners and SS-matrix poles of the one dimensional Rosen-Morse II Hamiltonian

Among the list of one dimensional solvable Hamiltonians, we find the Hamiltonian with the Rosen-Morse II potential. The first objective is to analyze the scattering matrix corresponding to this potential. We show that it includes a series of poles corresponding to the types of redundant poles or anti-bound poles. In some cases, there are even bound states and this depends on the values of given parameters. Then, we perform different supersymmetric transformations on the original Hamiltonian using the ground state (for those situations where there are bound states) wave functions, or other wave functions that comes from anti-bound states or redundant states. We study the properties of these transformations.Comment: 20 pages, 6 figure

Factorizations of one dimensional classical systems

A class of one dimensional classical systems is characterized from an algebraic point of view. The Hamiltonians of these systems are factorized in terms of two functions that together with the Hamiltonian itself close a Poisson algebra. These two functions lead directly to two time-dependent integrals of motion from which the phase motions are derived algebraically. The systems so obtained constitute the classical analogues of the well known factorizable one dimensional quantum mechanical systems.Comment: 19 pages, 7 figure