Nonlinear Phenomena in Complex Systems, 2011, Vol.14, No.1, pp.14-26

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2011, Vol.14, No.1, pp.14-26

Quantum Kepler Problem for Spin 1/2 Particle in Spaces on Constant Curvature. I. Pauli Theory.
E. M. Ovsiyuk

Transition to a nonrelativistic Pauli equation in Riemann space of constant positive curvature for a Dirac particle in presence of the Coulomb field is performed in the system of radial equations, exact solutions are constructed in terms of Hein functions, the energy spectrum is derived. The same is done for the Kepler quantum problem in hyperbolic Lobachevsky space, solutions are constructed in terms of Hein functions, the energy spectrum is obtained.
Key words: Pauli equation, spaces of constant curvature, bound states, Coulomb field

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