An overview of Schrِdinger-Poisson problems

Recent advances to the “Wigner-Poisson” problem are presented. Existence, uniqueness, and regularity of solutions is shown in various settings; these include periodic, stationary, and ‘mixed’ boundary value problems. Results for Wigner equations modified to describe dissipation and nonlinear field effects are also presented; finally, conditions for the existence of a classical limit to the Wigner function are discussed.