JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES. INST MECHANICS CONTINUA & MATHEMATICAL SCIENCES. 2019. P. 642-650
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 hyper-geometric 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.