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On a generalized oscillator system: Interbasis expansions
Author(s) -
Kibler Maurice,
Mardoyan Levon G.,
Pogosyan George S.
Publication year - 1997
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1997)63:1<133::aid-qua17>3.0.co;2-d
Subject(s) - harmonic oscillator , wave function , isotropy , prolate spheroidal coordinates , basis (linear algebra) , recursion (computer science) , quantum , physics , mathematical physics , morse potential , eigenfunction , classical mechanics , spherical harmonics , prolate spheroid , quantum mechanics , mathematics , geometry , eigenvalues and eigenvectors , algorithm
This article deals with a nonrelativistic quantum mechanical study of a dynamical system which generalizes the isotropic harmonic oscillator system in three dimensions. The Schrödinger equation for this generalized oscillator system is separable 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 found to be analytic continuations (to real values of their arguments) of Clebsch‐Gordan 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 oscillator system (projected on the z‐line) and the Morse system (in one dimension) is discussed. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 133–148, 1997