Green function of electron in a quantized wave field

Green function for electron in the field of a quantum wave, which is necessary for accounting the interaction with other fields in the second and higher orders of the perturbation theory, has been found. The simplest case of a monochromatic quantized wave is under consideration. The calculation of Green function makes it possible to clear up to some extent the meaning of the 'forbidden' zone. And, at last, with Green function it is possible to find the way of obtaining the orthonormal complete system of electron wave function in the field of the quantized wave; which satisfy the natural asymptotic initial conditions: at t → -infinity these functions coincide with the free electron wave functions