Geodesic
Quantum mechanics for a vector particle with quadrupole moment in the external uniform magnetic field
Problemy fiziki, matematiki i tehniki, no. 3 (2017), pp. 18-27.

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On the base of the matrix $10$-dimensional formalism, behavior of a vector particle with a quadrupole moment is studied in presence of external uniform magnetic field. Three series of the energy levels related to bound states of the particle are found. To assign them physical sense for all values of the main quantum number $n = 0,1,2,\dots$ one must impose special restrictions on quadrupole moment — they are formulated explicitly. Also, the problem of a neutral vector particle with quadrupole moment in presence of magnetic field is studied. At this, solutions of three types are constructed in terms of Bessel functions, in each case the influence of the quadrupole moment consists in presence of a scale factor $\mu$ in the argument $x=\mu r$ of the functions, which depends on the quadrupole moment parameter and magnitude of the uniform magnetic field.
Keywords: vector particle, magnetic field, Duffin–Kemmer formalism, separation of the variables
Mots-clés : quadrupole moment, exact solutions. 
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     title = {Quantum mechanics for a vector particle with quadrupole moment in the external uniform magnetic field},
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V. V. Kisel; E. M. Ovsiyuk; Y. A. Voynova; V. M. Red'kov. Quantum mechanics for a vector particle with quadrupole moment in the external uniform magnetic field. Problemy fiziki, matematiki i tehniki, no. 3 (2017), pp. 18-27. http://geodesic.mathdoc.fr/item/PFMT_2017_3_a2/

[1] A. A. Bogush, L. G. Moroz, Vvedenie v teoriyu klassicheskikh polei, Nauka i tekhnika, Minsk, 1968, 386 pp.

[2] E. M. Ovsiyuk, Ya. A. Voynova, V. V. Kisel, V. Balan, V. M. Red'kov, “Spin 1 Particle with Anomalous Magnetic Moment in the External Uniform Electric Field”, Quaternions: Theory and Applications, ed. Sandra Griffin, Nova Science Publishers, Inc., USA, 2017, 47–84

[3] V. Kisel, Ya. Voynova, E. Ovsiyuk, V. Balan, V. Red'kov, “Spin 1 Particle with Anomalous Magnetic Moment in the External Uniform Magnetic Field”, NPCS, 20:1 (2017), 21–39 | Zbl