Coherent states for Smorodinsky-Winternitz potentials

Unal N.

CENTRAL EUROPEAN JOURNAL OF PHYSICS, vol.7, no.4, pp.774-785, 2009 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 4
  • Publication Date: 2009
  • Doi Number: 10.2478/s11534-009-0039-3
  • Journal Name: CENTRAL EUROPEAN JOURNAL OF PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.774-785
  • Keywords: coherent states, path integrals, deformed harmonic oscillators, HAMILTONIAN-SYSTEMS, EUCLIDEAN-SPACE, SUPERINTEGRABILITY, FREEDOM, NUCLEI, MOTION
  • Akdeniz University Affiliated: No

Abstract

In this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations of the two-dimensional harmonic oscillator problem. In the first case, we find the non-spreading wave packets by transforming the system into four oscillators in Cartesian, and also polar, coordinates. In the second case, the coherent states are constructed in Cartesian coordinates by transforming the system into three non-isotropic harmonic oscillators. All of these states evolve in physical-time. We also show that in parametric-time, the second case can be transformed to the first one with vanishing eigenvalues.