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The Wigner-Poisson problem in a crystal. (English) Zbl 0822.58070
Summary: We present a model for the transport of electrons in semiconductors. The model consists of an energy-band version of the Quantum Liouville (Wigner) equation coupled to a discrete Poisson equation.

58Z05 Applications of global analysis to the sciences
82D55 Statistical mechanical studies of superconductors
Full Text: DOI
[1] Ashcroft, N. W.; Mermin, N. D., Solid State Physics (1976), Holt-Saunders International Edition · Zbl 1118.82001
[2] Bertsch, G. F., Heavy Ion Dynamics of Intermediate Energy, Manuscript (1980), Cyelotron Laboratory and Physics Department, Michigan State University: Cyelotron Laboratory and Physics Department, Michigan State University East Lansing Michigan 48824, USA
[3] Degond, P.; Markowich, P. A., A Quantum Transport model for semiconductors: The Wigner - Poisson problem on a bounded Brillouin zone, manuscript (1988)
[4] Hittmair, O., Lehrbuch der Quantenmechnaik, Verlag Karl Thiemig (1970), München
[5] Klucksdahl, N. C.; Kriman, A. M.; Ferry, D. K.; Ringhofer, C., Self consistent study of the Resonant Tunneling Diode, Phys. Review (1988), submitted to
[6] Landau, L. D.; Lifschitz, E. M., Lehrbuch der Theoretischen Physik III: Quantenmechanik, Akademieverlag (1966), Berlin · Zbl 0144.23805
[7] Markowich, P. A., On the Equivalence of the Schrödinger and the Quantum Liouville Equations, Math. Meth. in Appl. Sci. (1988), to appear in
[8] Tatarskii, V. I., The Wigner Representation of Quantum Mechanics, Sov. Phys. Usp., Vol. 26, Nr. 4, 311-327 (1983)
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