An inverse scattering problem for the Schr\"{o}dinger equation in a semiclassical process
Nicoleau, François
arXiv, 0512034 / Harvested from arXiv
We study an inverse scattering problem for a pair of Hamiltonians $(H(h), H\_0 (h))$ on $L^2 (\r^n)$, where $H\_0 (h) = -h^2 \Delta$ 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 $\lambda >0$, determine the potential $V$ at infinity.
Publié le : 2005-12-12
Classification:  Mathematical Physics,  81U40
@article{0512034,
     author = {Nicoleau, Fran\c cois},
     title = {An inverse scattering problem for the Schr\"{o}dinger equation in a
  semiclassical process},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0512034}
}
Nicoleau, François. An inverse scattering problem for the Schr\"{o}dinger equation in a
  semiclassical process. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0512034/