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

François Nicoleau
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Abstract

We study an inverse scattering problem for a pair of Hamiltonians $(H(h), H\_0 (h))$ on $L^2 (\r^n)$, where $H\_0 (h) = -h^2 Δ$ 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 $n \geq 3$, the knowledge of the scattering operators $S(h)$, $h \in ]0, 1]$, up to $O(h^\infty)$ in ${\cal{B}} (L^2(\r^n))$, and which are localized near a fixed energy $λ>0$, determine the potential $V$ at infinity.

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François Nicoleau. 2005-12-12. An inverse scattering problem for the Schrödinger equation in a semiclassical process. https://arxiv.org/abs/math-ph/0512034

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