Semiclassical estimates on resolvents of Schrödinger operators with homogeneous electric field

Abstract

We are interested in the limiting absorption principle for Schrödinger operators of the form: H(h) = -h2Δ + x1 + V(x), 0 < h ≤ h0. For a large class of potentials V, we establish various estimates for the resolvents of H(h) at non-trapping energy. The proof is based on a simple commutator technique. Our results seem to be new even in the case of h = 1. © 1989.