Theory of the Free-Electron Laser: from classical to quantum

All present realizations of a free-electron laser (FEL) can be solely described by classical physics. In this thesis, however, we are dealing with a parameter regime in which quantum effects become important. When the discrete recoil, an electron experiences during its interaction with the fields determines the dynamics we speak of the 'quantum regime' or simply of a 'Quantum FEL'. In this limiting case, the electrons occupy only two resonant momentum levels. The aim of this thesis is to investigate, both, the transition area between classical physics and quantum mechanics in the FEL, as well as to extend previous models for the extreme quantum domain and to compare its properties with those of its classical counterpart.