Decay for time-dependent Schroedinger equations

We study the decay in time of solutions of Schrodinger equations of the type du/du=idelta u+iV(t)u, establishing that for small potentials and initial data in L1 the solution u satisfies sup[u(x,t)](x element of R)<const * t^-n/2. In the process we also develop a number of results on operators of evolution; i.e., on the existence of solutions of the abstract initial value problem du/dt=A(t)u,u(0)=u0 where u0 element of X, X a Banach space, A(t) an operator in X for each t, and the
solution is an X-valued function u.