On a Generalized Oscillator: Invariance Algebra and Interbasis Expansions

Details On a Generalized Oscillator: Invariance Algebra and Interbasis Expansions On a Generalized Oscillator: Invariance Algebra and Interbasis Expansions

1997-12-05

arxiv.org/abs/quant-ph/9712014v1

Phys.Atom.Nucl.61:1782-1788,1998; Yad.Fiz.61:1893-1899,1998

Physics

Quantum Physics

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

Scientific paper

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.

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