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On a generalized oscillator system: Interbasis expansions

✍ Scribed by Maurice Kibler; Levon G. Mardoyan; George S. Pogosyan

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
221 KB
Volume
63
Category
Article
ISSN
0020-7608

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✦ Synopsis

This article deals with a nonrelativistic quantum mechanical study of a dynamical system which generalizes the isotropic harmonic oscillator system in three dimensions. The Schrodinger equation for this generalized oscillator system is separable ¨Ž . in spherical, cylindrical, and spheroidal prolate and oblate coordinates. The quantum mechanical spectrum of this system is worked out in some details. The problem of interbasis expansions of the wave functions is completely solved. The coefficients for the expansion of the cylindrical basis in terms of the spherical basis, and vice versa, are Ž . found to be analytic continuations to real values of their arguments of Clebsch᎐Gordan Ž . coefficients for the group SU 2 . The interbasis expansion coefficients for the prolate and oblate spheroidal bases in terms of the spherical or the cylindrical bases are shown to satisfy three-term recursion relations. Finally, a connection between the generalized Ž . Ž . oscillator system projected on the z-line and the Morse system in one dimension is discussed.

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