Absolute continuity of positive spectrum for Schrödinger operators with long-range potentials

Abstract

Absolute continuity in (0, ∞) for Schrödinger operators − Δ + V( x), with long range potential V = V 1 + V 2 such that ∂V 1 ∂ r , V 2 = 0(r −1−ϵ) , ϵ > 0, as ¦ x ¦ → ∞, is shown by proving estimates on resolvents near the real axis. Completeness of the modified wave operators for a superposition of Coulomb potentials also follows. Singular local behavior of V is allowed.