  In a quantum mechanical description of the free-electron laser (FEL) the
electrons jump on discrete momentum ladders, while they follow continuous
trajectories according to the classical description. In order to observe the
transition from quantum to classical dynamics, it is not sufficient that many
momentum levels are involved. Only if additionally the initial momentum spread
of the electron beam is larger than the quantum mechanical recoil, caused by
the emission and absorption of photons, the quantum dynamics in phase space
resembles the classical one. Beyond these criteria, quantum signatures of
averaged quantities like the FEL gain might be washed out.
