Abstract
The Dirac equation is considered for an electron in a constant homogeneous magnetic field and in a quantized electromagnetic plane wave propagating along the direction of the former. This problem is shown to be reduced to the Schrodinger equation for a system of many interacting oscillators. The corresponding Hamiltonian is diagonalized. An equation is established relating the total energy with the moment of a system along the magnetic field. Approximate solutions of this equation are given. A behaviour of a system close to cyclotron resonance is discussed.
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