Jose CARINENA
Departamento de Fisica Teorica,
Facultad de Ciencias,
Universidad de Zaragoza,
Zaragoza 50009,
SPAIN
E-mail: jfc@unizar.es

Generalized oscillators, isochronous systems and equispaced spectra

Abstract:
We discuss several generalizations of the harmonic oscillator each one preserving some specific characteristics of the harmonic oscillator, either superintegrability and Hamilton-Jacobi separability, or isochronicity or equispacing of spectra in the classical and quantum approaches.

  1. J.F. Carinena, M.F. Ranada, M. Santander and M. Senthilvelan, A non-linear Oscillator with quasi-Harmonic behaviour: two- and $n$-dimensional Oscillators, Nonlinearity 17 (2004), 1941-1963; math-ph/0406002.
  2. J.F. Carinena, M.F. Ranada and M. Santander, One-dimensional model of a Quantum non-linear Harmonic Oscillator, Rep. Math. Phys. 54 (2004), 285-293.
  3. J.F. Carinena, M.F. Ranada and M. Santander, Lagrangian formalism  for nonlinear second-order Riccati systems: one-dimensional integrability and wo-dimensional superintegrability, J. Math. Phys. 46 (2005),  062703.