Spin 1/2 Particle with Two Masses in External Magnetic Field

Abstract

Equation for spin 1/2 particle with two mass states is investigated in presence of magnetic field. The problem reduces to a system of 4 linked 2-nd order differential equations. After diagonalization of the mixing term, separate equations for four different functions are derived, in which the spectral parameters coincide with the roots of a 4-th order polynomial. Solutions are constructed in terms of confluent hypergeometric functions; four series of energy spectrum are found. Numerical study of the spectra is performed. Physical energy levels for the two mass fermion differ from those for the ordinary Dirac fermion.