QUANTUM THEORY OF HIGH-GAIN FREE-ELECTRON LASERS *

We formulate a quantum linear theory of the N-particle free-electron laser Hamiltonian model, quantizing both the radiation field and the electron motion, in the steady state regime. Quantum effects such as frequency shift, line narrowing, quantum limitation for bunching and energy spread and minimum uncertainty states are described. Using a second quantization formalism we demonstrate quantum entanglement between the recoiling electrons and the radiation field.