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Asymptotic completeness for N-body short-range quantum systems: A new proof. (English) Zbl 0726.35096
The author gives a new and shorter proof of the asymptotic completeness for N-body short-range quantum systems. The main originality of this work is in the way of proving a crucial propagation estimate, using some boosted time-dependent Hamiltonian, involving a real-valued phase function: \[ K(t)=(p-v(x,t))^ 2+V(x) \] with v(x,t) close to x/2t.
This permits to show that the intercluster motion \(P_ a\) behaves asymptotically as \(x_ a/2t\) for a given cluster decomposition a.

MSC:
35P25 Scattering theory for PDEs
81U10 \(n\)-body potential quantum scattering theory
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