The Wigner function for thermal equilibrium

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. © 1991 Birkhäuser Verlag.