An inverse scattering problem for the Schrödinger equation in a semiclassical process

2005/12/12 by François Nicoleau, Nicoleau, François
Mathematics · Physics and Astronomy · #81U40 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:81U40

paper · pdf · doi:10.48550/arxiv.math-ph/0512034

9 pages

arxiv created 2005/12/12 · arxiv updated 2009/12/01

Abstract

We study an inverse scattering problem for a pair of Hamiltonians (H(h), H_0 (h)) on L² (\rⁿ), where H_0 (h) = -h² Δ and H (h)= H_0 (h) +V, V is a short-range potential with a regular behaviour at infinity and h is the semiclassical parameter. We show that, in dimension n ≥ 3, the knowledge of the scattering operators S(h), h ∈ ]0, 1], up to O(h^∞) in \calB (L²(\rⁿ)), and which are localized near a fixed energy λ>0, determine the potential V at infinity.

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