Transition Layer of the Relativisyic Strophotron

The Klein-Gordon equation of motion in the transition layer of a free-electron laser of the relativistic strophotron type is studied. The condition of suddenly switching-on interaction is found: a smallness of the transition layer at the entrance compared to the distance traveled by the electron in longitudinal direction in one period of transverse oscillations in strophotron. The results are correspond to the results of classical description. It is shown, that in an electric strophotron, under the assumption of a suddenly switching-on interaction, the transverse energy of an electron at the moment t = 0 undergoes a jump. However, the total energy is conserved, because at the same moment t = 0, the longitudinal energy of the electron has the same jump with opposite sign.