Soffer, Avy On the many body problem in quantum mechanics. (English) Zbl 0809.47009 Robert, D. (ed.), Méthodes semi-classiques. Vol. 1. École d’été (Nantes, juin 1991). Paris: Société Mathématique de France, Astérisque. 207, 109-152 (1992). The article gives a review on the techniques used in modern mathematical scattering theory of quantum mechanical \(N\)-body systems. Some of the topics are: microlocal propagation theory, possible partitions of unity, kinematics, expansion of commutators, further spectral properties. Most of the proofs are sketched. For an interested reader a detailed list of references gives a good overview on the recent literature.For the entire collection see [Zbl 0773.00029]. Reviewer: M.Demuth (Clausthal) Cited in 1 Document MSC: 47A40 Scattering theory of linear operators 35P25 Scattering theory for PDEs 81U10 \(n\)-body potential quantum scattering theory 46L51 Noncommutative measure and integration 46L53 Noncommutative probability and statistics 46L54 Free probability and free operator algebras Keywords:mathematical scattering theory of quantum mechanical \(N\)-body systems; microlocal propagation theory; partitions of unity; kinetics; expansion of commutators PDFBibTeX XMLCite \textit{A. Soffer}, in: Méthodes semi-classiques. Vol. 1. École d'été (Nantes, juin 1991). Paris: Société Mathématique de France. 109--152 (1992; Zbl 0809.47009)