Nonlinear Phenomena in Complex Systems, 2017, Vol.20, No.1, pp.21-39

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2017, Vol.20, No.1, pp.21-39

Spin 1 Particle with Anomalous Magnetic Moment in an External Uniform Magnetic Field
V. Kisel, Ya. Voynova, E. Ovsiyuk, V. Balan, and V. Red'kov

Within the matrix 10-dimensional Duffin–Kemmer (DK) formalism applied to the Shamaly–Capri field, we study the behavior of a vector particle with anomalous magnetic moment in åðó presence of an external uniform magnetic field. The separation of variables in the wave equation is performed using projective operator techniques and the theory of DK-algebras. The problem is reduced to a system of 2-nd order differential equations for three independent functions, which is solved in terms of confluent hypergeometric functions. Three series of energy levels are found, two of which substantially differ from those for spin 1 particles without anomalous magnetic moment. For assigning them physical sense for all the values of the main quantum number n = 0, 1, 2, . . ., one has to impose special restrictions on a parameter related to the anomalous moment. Otherwise, only some part of the energy levels corresponds to the bound states. The neutral spin 1 particle is considered as well. In this case no bound states exist in the system, and the main qualitative manifestation of the anomalous magnetic moment consists in occurrence of a space scaling of arguments of the wave functions, compared to a particle without such a moment. Also we give some details of the general theory of the Shamaly–Capri particle; in particular, we describe some features of this theory extended to General Relativity.

Key words: Duffin–Kemmer algebra, projective operators, spin 1 particle, anomalous magnetic moment, magnetic field, exact solutions, bound states

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