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Exact spectrum for quantum oscillator in spaces of constant curvature from WKB-quantization

Quantum-mechanical WKB-method is elaborated for the known quantum oscillator problem in curved 3-spaces models Euclid, Riemann, and Lobachevsky E_{3}, H_{3}, S_{3} in the framework of the complex variable function theory. Generalized generally covariant Schrödinger equation is considered. In all three space models, exact energy levels are found with the help of constructing special formal WKB-sieries.

preprint2010arXivOpen access
E. M. OvsiyukV. M. Red'kov
math-phmath.MPquant-ph
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E. M. OvsiyukV. M. Red'kov

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