Comportement asymptotique semiclassique de l'amplitude de diffusion pour des perturbations captivesSemi-classical behavior of the scattering amplitude for trapping perturbations

We study the semi-classical behavior when h→0, of the scattering amplitude f(θ,ω,λ,h) associated to the Schrödinger operator $\text{P(h)=?}\text{1}\text{2}\text{h}{}^2\text{Δ+V(x)}$ for short range perturbations V(x). We show that if we modify the potential V(x) in a domain contained in {x:V(x)>λ}, the scattering amplitude f(θ,ω,λ,h) is changed by a term of order O(h^∞). Moreover, under an additional escape assumption, we get an asymptotics of the scattering amplitude. To cite this article: L. Michel, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 655–660.