Stimulated scattering of electrons by photons and adiabatic switching on hypothesis

The stimulated scattering of electrons by a standing light wave is considered. The amplitude of the standing wave is supposed to be slowly switched on and slowly switched off after the interaction. It is found that the scattering probability can be small due to the slowness of the switching-on process. The Kapitza-Dirac effect disappears in the adiabatic limit. The resonance scattering is considered which arises when another (running) light wave is added. The corresponding probability and the scattering directions have been derived.