English

On a Generalized Oscillator: Invariance Algebra and Interbasis Expansions

Quantum Physics 2011-04-15 v1 Mathematical Physics math.MP Atomic and Molecular Clusters Atomic Physics Chemical Physics

Abstract

This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D=2 and the coefficients connecting the Cartesian and cylindrical bases as well as the cylindrical and spherical bases for D=3. These interbasis expansion coefficients are found to be analytic continuations to real values of their arguments of the Clebsch-Gordan coefficients for the group SU(2). For D=2, the superintegrable character for the generalized oscillator system is investigated from the points of view of a quadratic invariance algebra.

Keywords

Cite

@article{arxiv.quant-ph/9712014,
  title  = {On a Generalized Oscillator: Invariance Algebra and Interbasis Expansions},
  author = {Y. M. Hakobyan and M. Kibler and G. S. Pogosyan and A. N. Sissakian},
  journal= {arXiv preprint arXiv:quant-ph/9712014},
  year   = {2011}
}

Comments

13 pages, Latex file. Submitted for publication to Yadernaya Fizika