The Quantum Mechanics of Many-Body Systems

The Quantum Mechanics of Many-Body Systems

1st Edition - January 1, 1961

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  • Author: D. J. Thouless
  • eBook ISBN: 9781483275963

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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.

Table of Contents

  • Preface

    I. Introduction

    Ii. Soluble Models

    1. Introduction

    2. Noninteracting Fermions and Bosons

    3. Second Quantization

    4. Harmonic Forces

    III. 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 Model

    IV. 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-Matrix

    V. 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 Model

    VI. 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 Properties

    VII. 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 Theory

    VIII. 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 Superconductors

    IX. Bosons

    1. Introduction

    2. Liquid Helium

    3. Phonons


    Subject Index

Product details

  • No. of pages: 186
  • Language: English
  • Copyright: © Academic Press 1961
  • Published: January 1, 1961
  • Imprint: Academic Press
  • eBook ISBN: 9781483275963

About the Author

D. J. Thouless

About the Editors

H. S. W. Massey

Keith A. Brueckner

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