A simple N-electron free-electron-laser (FEL) Hamiltonian is seen to define a (1+1)-dimensional quantum field theory. For large N, the FEL dynamics is shown to be solved by a single-electron Schrödinger equation in a self-consistent field. The fluctuations around such a Schrödinger wave function are shown to be O(1/ √N ) and computable by a perturbative strategy. A number of observations are also reported on the best strategy to solve the Schrödinger equation.

• Received 26 January 1988

DOI:https://doi.org/10.1103/PhysRevA.38.233