The Quantum Mechanical Three-Body Problem

Erich W. Schmid / Horst Ziegelmann
The quantum mechanical three-body problem. Edited by H.Stumpf.

(Vieweg tracts in pure and applied physics, vol.2). Oxford / Braunschweig, 1974,

217 pages, 49 Figures, Hardcover ISBN 3-528-08337-9 & ISBN 0-08-018240-2

From the back cover:

This volume is intended as an introduction to three body theory. Starting from the time-dependent Schroedinger equation, the formulation of the scattering problem is given, and the specific problems of the three-body theory are discussed in comparison to the two body theory. After a discussion of the inadequacies of the Lippmann-Schwinger equation, the Faddeev theory is developed in detail. A variety of methods for solving the Faddeev equations are given, with special attention to breakup reactions. Two methods that allow us to overcome the common restriction to separable potentials are extensively discussed - the quasi-particle method and the Pade technique. A separate chapter is devoted to variational methods applied to the time-independend Schroedinger equation and to the Faddeev equations. In the case of the Schroedinger equation, special attention is given to the boundary conditions for three-body fragmentation. The methods of hyperspherical harmonics and of sequential decay states, which deal with this additional complication are examined.

Preface:

One of the outstanding problems of classical physics was the three-body problem, namely, to solve Isaac Netwon's equations of motion for three interacting bodies. There is a similar problem in modern quatum mechanics, namely, to describe the motion of three interacting atomic or subatomic particlesby rigorous integral equations. L.D. Faddeev, in 1960, published the first work on this problem, Scattering Theory for a Three-Particle System, and since then a great deal of work has been done, the results of which are mainly available in original articles and reviews.

The present book originated from a course given by the authors in the summer semester 1972. It was felt that the student who wants to aquaint himself with the field should no longer have to work his way through the review articles and the original literature. Therefore, the course lectures were revised and expanded to this volume.

It is not the aim of this book to cover the field completely. For example, there are different formulations of the abstract theory, any of which can equally well serve as a mathematical basis for the theory. Those of S. Weinberg, L. Rosenberg, J.V. Noble, R.G. Newton, R. Sugar and R. Blankenbecler, and P.A. Kazaks and K.R. Greider, however, have been omitted, while that of Faddeev has been dealt with extensively. Emphasis, instead, has been placed on the various ways of getting from the abstract operator equations to numerical solutions and to data which can be compared with experimental results.

We hope that this book will make the field of three-particle physics more readiliy accessible to the interested student. We also hope that it will help the experimentalist to understand better how the theoretical data are derived.

We thank Dr. J. Schwager and Dr. F. Sohre for their critical reading of the manuscript and Mrs. Ch. Stiller for the typing. We also thank the authors of original papers for giving us permission to reproduce their figures.

Erich W. Schmid / Horst Ziegelmann

Erich W. Schmid / Horst Ziegelmann
The quantum mechanical three-body problem. Edited by H.Stumpf.

(Vieweg tracts in pure and applied physics, vol.2). Oxford / Braunschweig, 1974,

217 pages, 49 Figures, Hardcover ISBN 3-528-08337-9 & ISBN 0-08-018240-2

Ziegelmann, H. (2005). Albert Einstein – Leben und Werk (2. Auflage). Norderstedt: BoD.