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Research Report MRR97-042
Scattering matrices for the quantum n body problem
Andrew Hassell
Abstract:
Consider a generalized n body Schrödinger operator H
with very short range potentials.
In this note, we show that the free channel `geometric'
scattering matrix, defined via asymptotic expansions of generalized
eigenfunctions of H, coincides with the free channel `analytic'
scattering matrix defined via wave
operators. Along the way, we show that the free channel
generalized eigenfunctions of Herbst-Skibsted and Jensen-Kitada
coincide with the plane waves
constructed previously by the author if the potentials are very short range.
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