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.References
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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