Laboratoire J. A. Dieudonne, U.R.A. 168 du C.N.R.S. Universite de Nice, Parc Valrose, F-06034, Nice, France
Department of Mathematics, Arizona State University, Tempe, AZ 85287, U.S.A.
Abstract:
We derive the Schrödinger and the Wigner equations for electrons in a crystal in the presence of an external force via spectral projection techniques. It is shown that the mixing of energy bands, due to the external force, can be treated as a small perturbation. The corresponding single state fluid dynamical equation, the quantum hydrodynamical model in a crystal, is derived.