Isotropic oscillator in the space of constant positive curvature. Interbasis expansions

1997/10/31 by Ye. M. Hakobyan, G. S. Pogosyan, A. N. Sissakian +1 · 1 citation
Physics and Astronomy · Mathematics · #quant-ph #hep-th #math-ph #math.MP

paper · pdf

published as Phys. Atom. Nucl. 62 (1999) 623-637; Yad. Fiz . 62 (1999) 671-685 · 21 pages, LaTex

arxiv created 1999/07/12 · arxiv updated 2009/11/30

Abstract

The Schrödinger equation is thoroughly analysed for the isotropic oscillator in the three-dimensional space of constant positive curvature in the spherical and cylindrical systems of coordinates. The expansion coefficients between the spherical and cylindrical bases of the oscillator are calculated. It is shown that the relevant coefficients are expressed through the generalised hypergeometric functions ₄F₃ of the unit argument or 6_j Racah symbols extended over their indices to the region of real values. Limiting transitions to a free motion and flat space are considered in detail. Elliptic bases of the oscillator are constructed in the form of expansion over the spherical and cylindrical bases. The corresponding expansion coefficients are shown to obey the three-term recurrence relations.

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