Nonlinear Phenomena in Complex Systems, 2013, Vol.16, No.1, pp.42-50

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2013, Vol.16, No.1, pp.42-50

Nonrelativistic Approximation for Quasi-Planes Wave of a Spin 1 Particle in Lobachevsky Space
E. M. Ovsiyuk and K. V. Kazmerchuk

Spin 1 particle in Pauli approximation is investigated on the background of a curved space of constant negative curvature, Lobachevsky space. Nonrelativistic approximation is performed in the system of 10 equations resulted from separating the variables in Duffin-Kemmer equation specified in quasi-cartesian coordinates. The problem is solved exactly in Bessel functions, the quantum states are determined by four quantum numbers. The treatment is substantially based on the use of a generalized helicity operator in Lobachevsky space model.

Key words: spin 1 particle, Duffin-Kemmer equation, Pauli approximation, Lobachevsky space, generalized helicity operator

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