Spin 1 Particle with Anomalous Magnetic Moment in the Presence of Electric and Magnetic Fields: Solutions with Cylindric Symmetry

Abstract

In the present paper, a spin 1 particle with anomalous magnetic moment has been examined in the presence of external uniform electric field. A generalized 10-dimensional Duffin–Kemmer–Petiau equation is specified in cylindric coordinates (t, r, φ, z) and the corresponding tetrad. Solutions with cylindric symmetry are searched, we diagonalize operators of the energy and the third projection of the total angular momentum. First we derive the system of 10 first order differential equations for functions FA(r, z) = FA(r)FA(z), A = 1, . . . , 10. The use of the Fedorov–Gronskiy method permits us to express these ten functions FA(r) through only three independent new functions. After that we derive the system of 10 differential equations for functions FA(z) dependent on the coordinate z. This system is resolved by means of the method generalizing the known approach applied when solving the similar problem in Cartesian coordinates. In this way the system of tree differential equations of the second order is obtained. After diagonalization of the mixing matrix, the system is reduced to separated equations for two new independent functions. Then the solutions in terms of confluent hypergeometric functions are constructed.