  We prove the existence of solutions to the Schrodinger-Poisson system on a
time interval independent of the Planck constant, when the doping profile does
not necessarily decrease at infinity, in the presence of a subquadratic
external potential. The lack of integrability of the doping profile is resolved
by working in Zhidkov spaces, in space dimension at least three. We infer that
the main quadratic quantities (position density and modified momentum density)
converge strongly as the Planck constant goes to zero. When the doping profile
is integrable, we prove pointwise convergence.
