Scattering matrices for the quantum body problem

Author:
Andrew Hassell

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

Published electronically:
March 27, 2000

MathSciNet review:
1695024

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Abstract | References | Similar Articles | Additional Information

Let be a generalized 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 , 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

Email:
hassell@maths.anu.edu.au

DOI:
https://doi.org/10.1090/S0002-9947-00-02563-0

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