Isotropic oscillator in a space of constant positive curvature: Interbasis expansions
Abstract
The Schrödinger equation is thoroughly analysed for the isotropic oscillator in the threedimensional 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 threeterm recurrence relations.
 Publication:

Physics of Atomic Nuclei
 Pub Date:
 April 1999
 DOI:
 10.48550/arXiv.quantph/9710045
 arXiv:
 arXiv:quantph/9710045
 Bibcode:
 1999PAN....62..623H
 Keywords:

 Quantum Physics;
 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Mathematical Physics
 EPrint:
 21 pages, LaTex