Spin 1 Particle With Anomalous Magnetic Moment in External Uniform Electric Field, Solutions With Cylindrical Symmetry

Abstract

A generalized 10-dimensional Duffin–Kemmer–Petiau equation for spin 1 particle with anomalous magnetic moment is examined in cylindrical coordinates $(t,r,\varphi ,z)$ in the presence of the external uniform electric field oriented along the axis $z$. On solutions, we diagonalize operators of the energy and third projection of the total angular momentum. First, we derive the system of 10 equations in partial derivatives for functions $F_i(r,z)=G_i\left(r\right)H_i\left(z\right)(i=\overline{1,10})$. The use of the method based on the projective operators permits us to express 10 variables $G_i\left(r\right)$ through only three different functions $f_1\left(r\right),f_2\left(r\right),f_3\left(r\right)$, which are solved in Bessel functions. After that, we derive the system of 10 first-order differential equations for functions $H_i\left(z\right)$. This system reduces to one independent equation for a separate function and to the system of two linked equations for two remaining primary functions. This system after diagonalization of the mixing matrix gives two separated equations for new variables. All three equations for basic functions are solved in terms of the confluent hypergeometric functions. Thus, the complete system of solutions with cylindrical symmetry for the vector particle with anomalous magnetic moment in the presence of the external uniform electric field is found.