Abstract:
Wave functions are found for a system consisting of a charge plus the second-quantized
electromagnetic field of a plane wave. The plane wave is represented by an expansion with
respect to photons with definite momentum and polarization. The interaction between the
electron and all the photons of the wave is allowed for exactly. The problem is solved by
the method of canonical transformations of creation and annihilation operators without explicit
specification of the form of these operators. The properties of the solutions are
studied and their relation to the Volkov solutions is found.