  We treat some classes of stochastic partial differential equations of
Schr\"odinger type within the framework of white noise analysis, combined with
Wiener-It\^o chaos expansions and pseudodifferential operator methods. The
initial data and potential term of the Schr\"odinger operator are assumed to be
generalized stochastic processes that have both temporal and spatial
dependence. We prove that the equations under consideration have unique
solutions in the appropriate (intersections of weighted)
Sobolev-Kato-Kondratiev spaces.
