2003/09/18 by Tobias Kramer, Christian Bracher
Physics and Astronomy · #cond-mat
published as "Symmetries in Science XI", Kluwer 2004, editors B. Gruber et al, pp. 317-353 · 38 pages, 25 figures, to be published in the proceedings of the symposium "Symmetries in Science XIII", Bregenz, Austria (2003)
arxiv created 2003/09/18 · arxiv updated 2009/12/01
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.