José F. Cariñena, Manuel F. Rañada, Mariano Santander
Published 2005-05-10Version 1
We discuss a classical nonlinear oscillator, which is proved to be a superintegrable system for which the bounded motions are quasiperiodic oscillations and the unbounded (scattering) motions are represented by hyperbolic functions. This oscillator can be seen as a position-dependent mass system and we show a natural quantization prescription admitting a factorization with shape invariance for the $n=1$ case, and then the energy spectrum is found. Other isochronous systems which can also be considered as a generalization of the harmonic oscillator and admit a nonstandard Lagrangian description are also discussed.
Journal: Proceedings of 10th International Conference in MOdern GRoup ANalysis (Larnaca, Cyprus, 2004), 39-46
Two-dimensional space-time symmetry in hyperbolic functions
Bessel functions of integer order in terms of hyperbolic functions
Topological self-similarity on the random binary-tree model
