Relativistic Quantum States of an Electron with Anomalous Magnetic Moment in an Electromagnetic Wave Field and a Homogeneous Magnetic Field

The exact solution of the Dirac equation and the spectrum of electron quasi-energies in a superposition of the field of a circularly polarized electromagnetic wave and a homogeneous magnetic field parallel to the direction of wave propagation, are found taking into account the anomalous magnetic moment. It is found that taking account of the anomalous magnetic moment removes the spin degeneracy and that for intense fields the levels change radically. The shift of the radiation frequency due to the intensity of the wave field is found. This shift can be considerable.