Propagation in crossed electric and magnetic fields: The quantum source approach
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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.
38 pages, 25 figures, to be published in the proceedings of the symposium "Symmetries in Science XIII", Bregenz, Austria (2003)
38 pages, 25 figures, to be published in the proceedings of the symposium "Symmetries in Science XIII", Bregenz, Austria (2003)