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

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dc.creatorHakobyan, Ye. M.
dc.creatorPogosyan, G. S.
dc.creatorSissakian, A. N.
dc.creatorVinitsky, S. I.
dc.date1997-10-20
dc.date1999-07-12
dc.date.accessioned2026-07-07T06:14:29Z
dc.date.available2026-07-07T06:14:29Z
dc.descriptionThe 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 $_4F_3$ 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.
dc.description21 pages, LaTex
dc.identifierhttps://arxiv.org/abs/quant-ph/9710045
dc.identifierhttp://arxiv.org/abs/quant-ph/9710045
dc.identifierPhys. Atom. Nucl. 62 (1999) 623-637; Yad. Fiz . 62 (1999) 671-685
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/93479
dc.subjectQuantum Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleIsotropic oscillator in the space of constant positive curvature. Interbasis expansions
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