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.
CITATION STYLE
Kramer, T., & Bracher, C. (2004). Propagation in Crossed Electric and Magnetic Fields: The Quantum Source Approach. In Symmetries in Science XI (pp. 317–353). Springer Netherlands. https://doi.org/10.1007/1-4020-2634-x_16
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