The Wigner function for thermal equilibrium

  • H. Steinrück
  • F. Odeh
Original Papers


We provide a simple mathematical framework which is useful for a precise description of the thermal equilibrium Wigner function and for obtaining approximations to it in both cases of Boltzmann and Fermi Dirac statistics. Regular and singular asymptotic expansions of this Wigner function are derived and their validity shown for respectively smooth and discontinuous potentials. We also generalize some continuation methods, previously suggested for Boltzmann statistics, to the case of Fermi Dirac statistics.


Mathematical Method Asymptotic Expansion Thermal Equilibrium Wigner Function Precise Description 
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Wir entwickeln einen einfachen mathematischen Rahmen zur Beschreibung der Wignerfunktion für Elektronen im thermischen Gleichgewicht und zur Bestimmung von Näherungen sowohl für den Fall einer Boltzmann Statistik als auch für den Fall einer Fermi Dirac Statistik. Wir leiten reguläre und singuläre asymptotische Entwicklungen für glatte bzw. unstetige Potentiale her und zeigen ihre Gültigkeit. Schließlich verallgemeinern wir eine Fortsetzungsmethode zur Berechnung der Wignerfunktion im Falle einer Boltzmann Statistik auf den Fall einer Fermi Dirac Statistik.


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Copyright information

© Birkhäuser Verlag 1991

Authors and Affiliations

  • H. Steinrück
    • 1
  • F. Odeh
    • 1
  1. 1.T. J. Watson Research CenterIBMYorktown HeightsUSA

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