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arXiv quant-ph/97120141997-12-05quant-phmath-phmath.MPphysics.atm-clusphysics.atom-phphysics.chem-ph

On a Generalized Oscillator: Invariance Algebra and Interbasis Expansions

Y. M. Hakobyan, M. Kibler, G. S. Pogosyan, A. N. Sissakian

备注：: 13 pages, Latex file. Submitted for publication to Yadernaya Fizika
发表信息：: Phys.Atom.Nucl.61:1782-1788,1998; Yad.Fiz.61:1893-1899,1998

英文摘要：

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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