Nonlinear Phenomena in Complex Systems, 2003, Vol.6, No.2, pp.654-668

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2003, Vol.6, No.2, pp.654-668

On WKB-Quantization for Kepler Problem in Euclide, Riemann, and Lobachevsky 3-Spaces
V.M. Red'kov

Quantum mechanical WKB-method is elaborated for the known quantum Kepler problem in curved 3-space: 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.
Key words: quantum mechanics, curved space, WKB-method, Kepler problem

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