Vector particle with polarizability in the uniform magnetic field

There is a 15-component equation, which describes the vector particle with the additional electromagnetic characteristics – polarizability. We specify this equation in cylindrical coordinates and in presence of the external uniform magnetic field. After separating the variables, the system of 15 first-order differential equations in the polar coordinate is derived. To resolve this system, we apply the algebraization method. In this approach, the complete wave function is decomposed into the sum of three parts. Dependence of the components in each part is determined by only one corresponding function Fi(r); i = 1; 2; 3. We construct these three basic variables in terms of the confluent hypergeometric functions. There is a quantization rule for some spectral parameter exists. Additionally, there arises an algebraic homogenous system of 15 equations, which completely determines the structure of 15- component solutions. From vanishing the determinant of this linear system, we derive a cubic algebraic equation with respect to the energy parameter "2. Its solutions are found in analytical form and studied numerically. In this way, we have obtained three energy spectra. One does not depend on the polarizability parameter and the other two are substantially modified by this characteristics.