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Graf, Gian Michele

Asymptotic completeness for N-body short-range quantum systems: A new proof. (English) Zbl 0726.35096

Commun. Math. Phys. 132, No. 1, 73-101 (1990).
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.
Reviewer: A.Martinez (Villetaneuse)

Cited in 3 Reviews
Cited in 73 Documents

MSC:

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

Keywords:

asymptotic completeness; intercluster motion
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References:

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