Sigal, I. M.; Soffer, A. Asymptotic completeness of \(N\)-particle long-range scattering. (English) Zbl 0811.35091 J. Am. Math. Soc. 7, No. 2, 307-334 (1994). The authors prove asymptotic completeness for \(N\)-particle long-range systems with potential at infinity with a power of \(| x |\) of order greater or equal to \(1 - 2^{-N-2}\). Asymptotic clustering is used to reduce the problem involving an \((N+1)\)-particle Schrödinger operator to that involving a time-dependent operator.Subspaces of balistic and subbalistic propagation are characterized in terms of singular sets for (or the spectra of) appropriate asymptotic observables. Reviewer: M.Codegone (Torino) Cited in 12 Documents MSC: 35P25 Scattering theory for PDEs 47F05 General theory of partial differential operators 81U10 \(n\)-body potential quantum scattering theory Keywords:asymptotic clustering; subspaces of balistic and subbalistic propagation; Schrödinger operator PDFBibTeX XMLCite \textit{I. M. Sigal} and \textit{A. Soffer}, J. Am. Math. Soc. 7, No. 2, 307--334 (1994; Zbl 0811.35091) Full Text: DOI