On WKB-Quantization for Kepler Problem in Euclide, Riemann and Lobachevsky 3-Space

Details On WKB-Quantization for Kepler Problem in Euclide, Riemann and Lobachevsky 3-Space On WKB-Quantization for Kepler Problem in Euclide, Riemann and Lobachevsky 3-Space

2003-05-24

arxiv.org/abs/hep-th/0305214v1

Nonlin.Phenom.Complex Syst.6:654-668,2003

Physics

High Energy Physics

High Energy Physics - Theory

18 pages

Scientific paper

Quantum mechanical WKB-method is elaborated for the known quantum Kepler problem in curved 3-space models Euclide, Riemann and Lobachevsky in the framework of the complex variable function theory. Generalized Schr\"{o}dinger, Klein-Fock hydrogen atoms are considered. Exact energy levels are found and their exactness is proved on the base of exploration into $n$-degree terms of the WKB-series. Dirac equation is solved too, but only approximate energy spectrum is established.

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