A different approach to obtain Mayer’s extension to stationary single particle Wigner distribution
Anirban Bose, M. S. Janaki · Physics of Plasmas · 2012
It is shown that the stationary collisionless single-particle Wigner equation in one dimension containing quantum corrections at the lowest order is satisfied by a distribution function that is similar in form to the Maxwellian distribution with an effective mass and a generalized potential. The distribution is used to study quantum corrections to electron hole solutions.