Geodesic
Scattering theory: Some old and new problems
Documenta mathematica, ICM Berlin 1998, Vol. III (1998), pp. 87-96.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Scattering theory is, roughly speaking, perturbation theory of self-adjoint operators on the (absolutely) continuous spectrum. It has its origin in mathematical problems of quantum mechanics and is intimately related to the theory of partial differential equations. Some recently solved problems, such as asymptotic completeness for the Schrödinger operator with long-range and multiparticle potentials, as well as open problems, are discussed. We construct also potentials for which asymptotic completeness is violated. This corresponds to a new class of asymptotic solutions of the time-dependent Schrödinger equation. Special attention is paid to the properties of the scattering matrix, which is the main observable of the theory.
Classification : 35P25, 35J10, 81U20, 47A75
Keywords: wave operators, asymptotic completeness, $N$-particle Schrödinger operator, new channel of scattering, scattering matrix 
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     title = {Scattering theory: {Some} old and new problems},
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Yafaev, D. Scattering theory: Some old and new problems. Documenta mathematica, ICM Berlin 1998, Vol. III (1998), pp. 87-96. http://geodesic.mathdoc.fr/item/DOCMA_1998__S9__a69/