The quantum N-body problem

This selective review is written as an introduction to the mathematical the ory of the Schrodinger equation for N particles. Characteristic for these s ystems are the cluster properties of the potential in configuration space, which are expressed in a simple geometric language. The methods developed o ver the last 40 years to deal with this primary aspect are described by giv ing full proofs of a number of basic and by now classical results. The cent ral theme is the interplay between the spectral theory of N-body Hamiltonia ns and the space-time and phase-space analysis of bound states and scatteri ng states. (C) 2000 American Institute of Physics. [S0022-2488(00)01306-2].