%0 Journal Article
%T Propagation in crossed electric and magnetic fields: The quantum source approach
%A Tobias Kramer
%A Christian Bracher
%J Physics
%D 2003
%I arXiv
%X The propagation of electrons in static and uniform electromagnetic fields is a standard topic of classical electrodynamics. The Hamilton function is given by a quadratic polynomial in the positions and momenta. The corresponding quantum-mechanical problem has been analyzed in great detail and the eigenfunctions and time evolution operators are well-known. Surprisingly, the energy-dependent counterpart of the time-evolution operator, the Green function, is not easily accessible. However in many situations one is interested in the evolution of a system that started with emitted particles that carry a specific energy. In the following we present a suitable approach to study this type of matter waves arising from a localized region in space. Two applications are discussed, the photodetachment current in external fields and the quantum Hall effect in a fermionic electron gas.
%U http://arxiv.org/abs/cond-mat/0309424v1