Configuration space properties of S- matrix in scattering (*)

Amrein, W. O. ; Cibils, M. B. ; Sinha, K. B. (1987) Configuration space properties of S- matrix in scattering (*) Annales de l'Institut Henri Poincare, Section A - Physique Théorique, 47 (4). pp. 367-382. ISSN 0020-2339

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Official URL: http://archive.numdam.org/ARCHIVE/AIHPA/AIHPA_1987...

Abstract

We prove estimates on time decay for products of Schrodinger evolution groups between weighted L 2-spaces by using commutator techniques. These estimates are used to show that, for potentials V(x̲) decaying more rapidly than |x̲| -2, the scattering operator leaves a certain dense subset ~ of the domain of definition of Q̲2 invariant. This implies the existence of the global time delay (defined in terms of sojourn times) on ~ if V(x̲) = O(|x̲|-2-ε) at infinity, ε>0.

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