Semi‐classical limit of the scattering amplitude for trapping perturbations

Abstract

We study the semi‐classical asymptotic as h→0 of the scattering amplitude f(θ,ω,λ,h) associated to a Schrödinger operator H(h)=−½h²Δ+V(x) for short‐range trapping perturbations. Our main result yields the leading term of the integral of f(θ,ω,λ,h) for θ,ω∈Sⁿ⁻¹ fixed and λ∈[λ₀−ε,λ₀+ε], ε>0, λ₀>0, being a trapping energy level.