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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Scattering matrices for the quantum $N$ body problem
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by Andrew Hassell PDF
Trans. Amer. Math. Soc. 352 (2000), 3799-3820 Request permission

Abstract:

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
  • MR Author ID: 332964
  • Email: hassell@maths.anu.edu.au
  • Received by editor(s): February 11, 1998
  • Published electronically: March 27, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 352 (2000), 3799-3820
  • MSC (2000): Primary 35P25, 81U10, 81U20, 35S05
  • DOI: https://doi.org/10.1090/S0002-9947-00-02563-0
  • MathSciNet review: 1695024