Spin 1/2 Particle with Anomalous Magnetic Moment in a Uniform Magnetic Field

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