ua nt - p h / 97 12 01 4 v 1 5 D ec 1 99 7 On a Generalized Oscillator : Invariance Algebra and Interbasis Expansions
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چکیده
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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