Spin ½ particle with anomalous magnetic moment in presence of external magnetic field, exact solutions

Abstract

We examine a generalize Dirac equation for spin 1/2 particle with anomalous magnetic moment in presence of the external uniform magnetic field. After separation of the variables, the problem is reduced to a 4-order ordinary differential equation, which is solved exactly with the use of the factorization method. A generalized formula for Landau energy levels is found. Solutions are expressed in terms of confluent hypergeometric functions.