Scattering from local deformations of a semitransparent plane

We study scattering for the couple (AF,A0) of Schrödinger operators in L2(R3) formally defined as A0=−Δ+αδπjavax.xml.bind.JAXBElement@69b32f3e and AF=−Δ+αδπjavax.xml.bind.JAXBElement@45bf6b2b, α>0, where δπjavax.xml.bind.JAXBElement@656a861f is the Dirac δ-distribution supported on the deformed plane given by the graph of the compactly supported, Lipschitz continuous function F:R2→R and π0 is the undeformed plane corresponding to the choice F≡0. We provide a Limiting Absorption Principle, show asymptotic completeness of the wave operators and give a representation formula for the corresponding Scattering Matrix SF(λ). Moreover we show that, as F→0, ‖SF(λ)−1‖B(Ljavax.xml.bind.JAXBElement@7b000395(Sjavax.xml.bind.JAXBElement@bba1914))2=O(∫Rjavax.xml.bind.JAXBElement@3562cd7bdx|F(x)|γ), 0<γ<1.