ON A ONE-DIMENSIONAL SCHRODINGER-POISSON SCATTERING MODEL

A Schrodinger-Poisson model describing the stationary behavior of a qu antum device away from equilibrium is proposed and analyzed. In this m odel, current carrying scattering states of the Schrodinger equation a re considered. The potential is coupled to the Schrodinger equation th rough the density matrix defined according to a prescribed statistics. Existence of solutions is proven. The semiclassical limit is performe d via a Wigner transform which leads to the standard boundary value pr oblem for the semiclassical Vlasov-Poisson system. Finally, a high inj ection asymptotics is investigated.