Bloch electrons in an electric field

We use the Wigner distribution function and the Von Neumann equation to treat the problem of the evolution of Bloch electrons moving under the combined influence of a periodic potential and of ail applied continuous electric field. We show that our analysis provides ail efficient tool for the solution of the problem and incorporates, in a fairly natural way, the features of previous treatments. We discuss analogies with other dynamical systems, ruled by a periodic potential, as those relevant, to Free Electron Laser quantum interactions.