The topics in this volume include the ideas of mathematicians, physicists and chemists in the area of multiparticle scattering theory. Scattering theory (or collision theory as it is often called) is a fundamental area of theory and computation in both physics and chemistry. The correct formulation of scattering theory for two-body collisions is now well worked out, but systems with three or more particles still present fundamental unmet challenges, both in the formulations of the problem and in the interpretation of computational results. A key issue in the mathematical foundations is asymptotic completeness, which says that any state of a quantum system is a superposition of bound and scattering states. Key issues on the physical side are concerned with boundary conditions, electromagnetic fields, effective potentials and resonances.
From the contents: N-body quantum systems: A tutorial.- A tutorial on computational approaches to quantum scattering.- Time-independent wavepacket quantum mechanics.- Classical action and quantum N-body asymptotic completeness.- On trace formulas for Schroedinger-type operators.- Multiparticle quantum systems in constant magnetic fields.- New channels of scattering for two-and three-body quantum systems with long-range potentials.- State-of-state transition probabilities and control of laser- induced dynamical processes by the (t,t') Method.- Barrier resonances and chemical reactivity.- Quantization in the continuum-complex dilated expansions of scattering quantities.- Microscopic atomic and nuclear mean fields.- The Pauli principle in multi-cluster states of nuclei Nonperturbative approaches to atomic and molecular multiphoton.