Exchange effects in the Wigner-function approach

In this paper, an analysis of the Wigner function (WF) for identical fermions is presented. Three situations have been analyzed. i) A scattering process between two indistinguishable electrons in minimum uncertainty wavepackets showing the exchange and correlation hole in Wigner phase space. ii) An equilibrium ensemble of N electrons in a box showing that the WF integrated over space assumes the shape of a Fermi distribution even for very small N. iii) The reduced one-particle transport-equation for the WF in the case of interacting electrons showing the first contribution to the BBGKY hierarchy