Scattering matrices for the quantum N body problem
Date
2000
Authors
Hassell, Andrew
Journal Title
Journal ISSN
Volume Title
Publisher
American Mathematical Society
Abstract
Let H be a generalized N body Schrodinger operator with very short range potentials. Using Melrose's scattering calculus, it is shown that the free channel 'geometric' scattering matrix, defined via asymptotic expansions of generalized eigenfunctions of H, coincides (up to normalization) with the free channel 'analytic' scattering matrix defined via wave operators. Along the way, it is shown that the free channel generalized eigenfunctions of Herbst-Skibsted and Jensen-Kitada coincide with the plane waves constructed by Hassell and Vasy and if the potentials are very short range.
Description
Keywords
Keywords: N body problem; Scattering calculus; Scattering matrix; Scattering theory
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Source
Transactions of the American Mathematical Society
Type
Journal article