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Scattering matrices for the quantum $N$ body problem

Author: Andrew Hassell
Journal: Trans. Amer. Math. Soc. 352 (2000), 3799-3820
MSC (2000): Primary 35P25, 81U10, 81U20, 35S05
Published electronically: March 27, 2000
MathSciNet review: 1695024
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Let $H$ be a generalized $N$ body Schrödinger 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.

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Additional Information

Andrew Hassell
Affiliation: Centre for Mathematics and its Applications, Australian National University, Canberra ACT 0200, Australia

Keywords: $N$ body problem, scattering theory, scattering matrix, scattering calculus
Received by editor(s): February 11, 1998
Published electronically: March 27, 2000
Article copyright: © Copyright 2000 American Mathematical Society