The Runge-Lenz vector for quantum Kepler problem in the space of positive constant curvature and complex parabolic coordinates

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dc.creatorBogush, A. A.
dc.creatorOtchik, V. S.
dc.creatorRed'kov, V. M.
dc.date2006-12-17
dc.date.accessioned2026-07-07T07:35:37Z
dc.date.available2026-07-07T07:35:37Z
dc.descriptionBy analogy with the Lobachevsky space H_{3}, generalized parabolic coordinates (t_{1},t_{2},ϕ) are introduced in Riemannian space model of positive constant curvature S_{3}. In this case parabolic coordinates turn out to be complex valued and obey additional restrictions involving the complex conjugation. In that complex coordinate system, the quantum-mechanical Coulomb problem is stu- died: separation of variables is carried out and the wave solutions in terms of hypergeometric functions are obtained. At separating the variables, two parameters k_{1} and k_{2} are introduced, and an operator B with the eigen values (k_{1}+k_{2}) is found, which is related to third component of the known Runge-Lenz vector in space S_{3} as follows: i B = A _{3} + i \vec{L}^{2}, whereas in the Lobachevsky space as B =A_{3} + \vec{L}^{2}. General aspects of the possibility to employ complex coordinate systems in the real space model S_{3} are discussed.
dc.description10 pages, Proc. of 5th International Conference Bolyai-Gauss-Lobachevsky: Non-Euclidean Geometry In Modern Physics (BGL-5). 10-13 Oct 2006, Minsk, Belarus (pages 135-144)
dc.identifierhttps://arxiv.org/abs/hep-th/0612178
dc.identifierhttp://arxiv.org/abs/hep-th/0612178
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120155
dc.subjectHigh Energy Physics - Theory
dc.titleThe Runge-Lenz vector for quantum Kepler problem in the space of positive constant curvature and complex parabolic coordinates
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