The Quantum Mechanics of Many-Body Systems

1st Edition - January 1, 1961
Author: D. J. Thouless
Editors: H. S. W. Massey, Keith A. Brueckner
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 7 5 9 6 - 3

The Quantum Mechanics of Many-Body Systems provides an introduction to that field of theoretical physics known as ""many-body theory."" It is concerned with problems that are… Read more

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The Quantum Mechanics of Many-Body Systems provides an introduction to that field of theoretical physics known as ""many-body theory."" It is concerned with problems that are common to nuclear physics, atomic physics, the electron theory of metals, and to the theories of liquid helium three and four, and it describes the methods which have recently been developed to solve such problems. The aim has been to produce a unified account of the field, rather than to describe all the parallel methods that have been developed; as a result, a number of important papers are not mentioned. The main emphasis is on the theories of atomic nuclei, the electron gas, and liquid helium; there is no discussion of molecular theory or of solid helium. The reader is expected to be familiar with the principles of nonrelativistic quantum mechanics and of statistical mechanics, but a knowledge of field theory and a detailed knowledge of nuclear and solid state physics are not assumed.

PrefaceI. IntroductionIi. Soluble Models 1. Introduction 2. Noninteracting Fermions and Bosons 3. Second Quantization 4. Harmonic ForcesIII. Variational Methods 1. The Hartree-Fock Equations 2. The Self-Consistent Field for Atoms 3. The Thomas-Fermi Method 4. Nuclear Matter 5. The Hartree-Fock Equations for Extended Systems 6. Alternative Solutions of the Hartree-Fock Equations 7. Jastrow's Method 8. The Shell ModelIV. Perturbation Theory 1. General Discussion 2. The Goldstone-Hugenholtz Graphical Method 3. Wick's Theorem 4. Linked Graphs 5. Rules for Calculating with Graphs 6. Hartree-Fock Energies 7. Brueckner Theory 8. Brueckner Theory for Finite Nuclei 9. Divergence of the K-MatrixV. Low-Lying Excited States 1. Green's Functions and Collective Variables 2. One-Particle Green's Functions 3. Perturbation Calculation of Green's Functions 4. The Optical Model 5. The Fermi Liquid 6. Sound and Zero Sound 7. Collective Motion 8. Generator Coordinates 9. Two-Particle Green's Functions 10. Time-Dependent Hartree-Fock Theory 11. Application to the Shell ModelVI. Statistical Mechanics and Superconductivity Theory 1. The Partition Function 2. Free Fermions and Bosons 3. Superconductivity 4. Model of the Superconducting State 5. Superconducting State of a Real Metal 6. The Variational Principle for the Partition Function 7. Quasiparticle Method 8. Superfluidity of Liquid Helium Three 9. The Effect of Pairing on Nuclear PropertiesVII. Perturbation Theory at Finite Temperatures 1. The Bloch Equation 2. Linked Graph Expansion 3. Comparison with Ground State Perturbation Theory 4. Expectation Value of an Operator 5. Classical Limit of Perturbation TheoryVIII. Green's Functions at Finite Temperatures 1. Excited States at Finite Temperatures 2. Calculation of Green's Functions by Perturbation Theory 3. Plasma Oscillations 4. Correlation Energy 5. Screening 6. Survey of Alternative Techniques 7. Electrical Conductivity 8. Collective Modes in SuperconductorsIX. Bosons 1. Introduction 2. Liquid Helium 3. PhononsReferencesSubject Index