Schmid / Ziegelmann / Stumpf The Quantum Mechanical Three-Body Problem

Vieweg Tracts in Pure and Applied Physics
1. Auflage 2017
ISBN: 978-1-4831-6078-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 226 Seiten, Web PDF

The Quantum Mechanical Three-Body Problem deals with the three-body problem in quantum mechanics. Topics include the two- and three-particle problem, the Faddeev equations and their solution, separable potentials, and variational methods. This book has eight chapters; the first of which introduces the reader to the quantum mechanical three-body problem, its difficulties, and its importance in nuclear physics. Scattering experiments with three-particle breakup are presented. Attention then turns to some concepts of quantum mechanics, with emphasis on two-particle scattering and the Hamiltonian for three particles. The chapters that follow are devoted to the Faddeev equations, including those for scattering states and transition operators, and how such equations can be solved in practice. The solution of the Faddeev equations for separable potentials and local potentials is presented, along with the use of Padé approximation to solve the Faddeev equations. This book concludes with an appraisal of variational methods for bound states, elastic and rearrangement scattering, and the breakup reaction. A promising variational method for solving the Faddeev equations is described. This book will be of value to students interested in three-particle physics and to experimentalists who want to understand better how the theoretical data are derived.

Autoren/Hrsg.

Schmid, Erich W.

Ziegelmann, Horst

Stumpf, H.

Inhaltsverzeichnis

1;Front Cover;1
2;The Quantum Mechanical Three-Body Problem;4
3;Copyright Page;5
4;Table of Contents;7
5;Preface;6
6;Chapter 1. Introduction;10
6.1;1. Scattering Experiments with Three-Particle Breakup;11
6.2;2. Difficulties of the Theory;15
6.3;3. Importance of the Three-Body Problem in Nuclear Physics;19
7;Chapter 2. Some Concepts of Quantum Mechanics;23
7.1;1. The Two-Particle Problem;23
7.2;2. The Three-Particle Problem;41
8;Chapter 3. The Faddeev Equations;52
8.1;1. The Faddeev Equations for the T-Matrix;52
8.2;2. The Faddeev Equations for the Resolvent;60
8.3;3. The Faddeev Equations for Scattering States;61
8.4;4. The S-Matrix;63
8.5;5. The Faddeev Equations for Transition Operators;67
8.6;6. The Unitarity Relation;74
9;Chapter 4. Solution Methods for the Faddeev Equations;78
9.1;1. Partial Wave Decomposition of the Faddeev Equations;78
9.2;2. Some Concepts of the Theory of Integral Equations;83
9.3;3. Application to the Faddeev Equations;88
10;Chapter 5. Separable Potentials;90
10.1;1. Separable Potentials in the Two-Particle Problem;90
10.2;2. Solution of the Faddeev Equations for Separable Potentials;97
11;Chapter 6. Solution of the Faddeev Equations for Local Potential;131
11.1;1. Direct Solution of the Faddeev Equations for Local Potential;131
11.2;2. The Schmidt Method (Weinberg's Quasiparticle Method);135
11.3;3. The Quasiparticle Method in the Three-Particle Problem;142
12;Chapter 7. Solution of the Faddeev Equations by Padé Approximation;165
12.1;1. The Technique of Padé Approximation;165
12.2;2. Padé Approximation and Integral Equations;167
12.3;3. Padé Approximation and the Faddeev Equations;168
13;Chapter 8. Variational Methods;172
13.1;1. Variational Methods for Bound States;172
13.2;2. Variational Methods for Elastic Scatteringand for Multichannel Scattering;177
13.3;3. Variational Methods for Multichannel Scattering with Three-Particle Breakup;188
14;References;215
15;Index;225