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

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

1997-10-20

arxiv.org/abs/quant-ph/9710045v2

Phys. Atom. Nucl. 62 (1999) 623-637; Yad. Fiz . 62 (1999) 671-685

Physics

Quantum Physics

21 pages, LaTex

Scientific paper

The Schr\"odinger 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 $_4F_3$ 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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