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

V. M. Red'kov
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Abstract

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 Schrödinger, 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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V. M. Red'kov. 2003-05-24. On WKB-Quantization for Kepler Problem in Euclide, Riemann and Lobachevsky 3-Space. https://arxiv.org/abs/hep-th/0305214

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