Abstract
We prove that linear Schrödinger operators −Δ+q on a torus or on a bounded smooth domain in Rd, considered with Dirichlet boundary conditions, have a strongly nonresonant spectrum for any potential q of generic type (generic in the sense of Kolmogorov measure). As a consequence, a Krylov-Bogolyubov averaging theorem holds for nonlinear perturbations of the corresponding Schrödinger evolution equations.