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The quantum \(N\)-body problem. (English) Zbl 0981.81026
Summary: This selective review is written as an introduction to the mathematical theory of the Schrödinger equation for \(N\) particles. Characteristic for these systems are the cluster properties of the potential in configuration space, which are expressed in a simple geometric language. The methods developed over the last 40 years to deal with this primary aspect are described by giving full proofs of a number of basic and by now classical results. The central theme is the interplay between the spectral theory of \(N\)-body Hamiltonians and the space-time and phase-space analysis of bound states and scattering states.

MSC:
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81U10 \(n\)-body potential quantum scattering theory
47N50 Applications of operator theory in the physical sciences
81-03 History of quantum theory
81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
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