Quantum Mechanical Three-Body Problem (eBook)

Vieweg Tracts in Pure and Applied Physics

Erich W. Schmid, Horst Ziegelmann (Autoren)

H. Stumpf (Herausgeber)

eBook Download: PDF

2017 | 1. Auflage
226 Seiten
Elsevier Science (Verlag)
9781483160788 (ISBN)

Infos

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.

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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 Pade 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.

Inhalt

Front Cover 1
The Quantum Mechanical Three-Body Problem 4
Copyright Page 5
Table of Contents 7
Preface 6
Chapter 1. Introduction 10
1. Scattering Experiments with Three-Particle Breakup 11
2. Difficulties of the Theory 15
3. Importance of the Three-Body Problem in Nuclear Physics 19
Chapter 2. Some Concepts of Quantum Mechanics 23
1. The Two-Particle Problem 23
2. The Three-Particle Problem 41
Chapter 3. The Faddeev Equations 52
1. The Faddeev Equations for the T-Matrix 52
2. The Faddeev Equations for the Resolvent 60
3. The Faddeev Equations for Scattering States 61
4. The S-Matrix 63
5. The Faddeev Equations for Transition Operators 67
6. The Unitarity Relation 74
Chapter 4. Solution Methods for the Faddeev Equations 78
1. Partial Wave Decomposition of the Faddeev Equations 78
2. Some Concepts of the Theory of Integral Equations 83
3. Application to the Faddeev Equations 88
Chapter 5. Separable Potentials 90
1. Separable Potentials in the Two-Particle Problem 90
2. Solution of the Faddeev Equations for Separable Potentials 97
Chapter 6. Solution of the Faddeev Equations for Local Potential 131
1. Direct Solution of the Faddeev Equations for Local Potential 131
2. The Schmidt Method (Weinberg's Quasiparticle Method) 135
3. The Quasiparticle Method in the Three-Particle Problem 142
Chapter 7. Solution of the Faddeev Equations by Padé Approximation 165
1. The Technique of Padé Approximation 165
2. Padé Approximation and Integral Equations 167
3. Padé Approximation and the Faddeev Equations 168
Chapter 8. Variational Methods 172
1. Variational Methods for Bound States 172
2. Variational Methods for Elastic Scatteringand for Multichannel Scattering 177
3. Variational Methods for Multichannel Scattering with Three-Particle Breakup 188
References 215
Index 225

Produkt-Details

• Erscheint lt. Verlag: 31.1.2017
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Technik
• ISBN-13: 9781483160788 / 9781483160788