Three Body Problem

Presenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references.

The present volume represents the great majority of the papers presented on Sanibel Island at the first Symposium on Quantum Statistics and Many-Body Problems (January 26-29, 1975). In his Introductory Remarks, Professor Lawdin outlines the history of the original Symposia, and the genesis of the conference whose papers comprise this volume. We join him in his expression of thanks, and note, additionally, our gratitude to him and to Professors N. Y. Ohrn, J. R. Sabin, E. D. Adams, and John Daunt. The papers are grouped somewhat differently from their order of presentation. It seemed convenient to begin with the six papers which deal with sound propagation in one form or another, then have a two-paper diversion into solid Helium. The SHe superf1uid theme is picked up again with four papers on spin dynamics, orbit waves, etc., followed by a selection of five papers on a variety of experimental and theoretical aspects of the SHe superf1uid problem. Work in the areas of films, mono1ayers, and mixtures is presented next, followed by two papers on liquid ~He. We conclude with a selection of six papers on other quantum fluids and general statistical mechanics. We are most grateful to the contributors to this volume for their patience and cooperation; they have had as editors three utter novices! We have learned much, both scientifically and editorially. We hope that this volume will be of at least some help to others as well.

This brief book provides an overview of the gravitational orbital evolution of few-body systems, in particular those consisting of three bodies. The authors present the historical context that begins with the origin of the problem as defined by Newton, which was followed up by Euler, Lagrange, Laplace, and many others. Additionally, they consider the modern works from the 20th and 21st centuries that describe the development of powerful analytical methods by Poincare and others.

The four articles of the present volume address very different topics in nuclear physics and, indeed, encompass experiments at very different kinds of exp- imental facilities.

This book presents an overview of the different few-body techniques developed in nuclear physics and their applications to explore the structural properties of neutron-rich unstable nuclei, the so-called halo nuclei. Formal theory of two- and three-body scattering are discussed in a compact and abridged form to initiate the beginners who want to investigate the problems of halo nuclei within the framework of three-body models.

This is a textbook in the classical fashion with examples and ample homework problems. The material is arranged so that two or three different university courses at different academic levels can be based upon it. This text can be used as a basis for continuing education short courses or independent self study.

This book provides a systematic study of spectral and scattering theory for many-body Schrödinger operators at two-cluster thresholds. While the two-body problem (reduced after separation of the centre of mass motion to a one-body problem at zero energy) is a well-studied subject, the literature on many-body threshold problems is sparse. However, the authors’ analysis covers for example the system of three particles interacting by Coulomb potentials and restricted to a small energy region to the right of a fixed nonzero two-body eigenvalue. In general, the authors address the question: How do scattering quantities for the many-body atomic and molecular models behave within the limit when the total energy approaches a fixed two-cluster threshold? This includes mapping properties and singularities of the limiting scattering matrix, asymptotics of the total scattering cross section, and absence of transmission from one channel to another in the small inter-cluster kinetic energy region. The authors’ principal tools are the Feshbach–Grushin dimension reduction method and spectral analysis based on a certain Mourre estimate. Additional topics of independent interest are the limiting absorption principle, micro-local resolvent estimates, Rellich- and Sommerfeld-type theorems and asymptotics of the limiting resolvents at thresholds. The mathematical physics field under study is very rich, and there are many open problems, several of them stated explicitly in the book for the interested reader.