Spin 3/2 Particle in External Uniform Magnetic Field, the Method of Projective Operators

Abstract

In the present paper, an algebraic method for solving the system of equations describing the spin 3/2 particle in the presence of uniform magnetic field has been elaborated. The method is based on decomposition of 16-components wave function with transformation properties of vector-bispinor in the sum of four constitutes, which are determined by four projective operators. With the use of formalism of elements of complete matrix algebra the system is transformed to the form, in which only projective constituents 1/2 3/2 ( ), ( ) x x     enter. This system of equations is transformed to cylindric coordinates. On the wave functions three operators are digitalized: of energy, third projection of linear momentum, third projection of the total angular momentum. After separating the variables, we derive 4 linked subsystems of equations for 16-component functions 1/2 ( ), r   3/2 ( )r   . After performing needed calculations, the problem reduces to four independent second order equations for four primary functions. These equations are solved in terms of confluent hypergeometric functions, four different energy spectra are found.