Relativistic quantum states of a particle in an electromagnetic plane wave and a homogeneous magnetic field

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Abstract
The exact solutions of the Klein-Gordon and Dirac equations are found by purely algebraic procedures for a charged particle embedded simultaneously in a plane-wave radiation field and in a uniform magnetic field which is directed parallel to the direction of propagation of the plane wave. Two cases of the solutions are considered: (i) the radiation field is a classical external plane wave and (ii) it is a quantized field. The connection with less explicit or more specific solutions of this problem known previously is established and possible applications are discussed.