Quantum Theory of the Solid State

Quantum Theory of the Solid State

1st Edition - June 28, 1976

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  • Author: Joseph Callaway
  • eBook ISBN: 9780323142250

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Quantum Theory of the Solid State, Student Edition, describes the concepts and methods, and introduces some of the central problems of the quantum theory of solids. It should be suitable as a textbook for students who have completed a one-year course in quantum mechanics and have some familiarity with the experimental facts of solid state physics. It should also be useful as a reference work. The book is organized into two parts. Part A contains much of the formalism required for the theoretical study of solids; Part B is oriented toward more specific problems. Thus, Part A includes phenomenological treatments of lattice vibrations and magnetic order, a discussion of symmetry groups, and a description of the properties of one-electron wave functions and the principal techniques for calculating energy levels. In Part B the machinery developed previously is applied to impurities, disordered systems, the effects of external fields, and transport phenomena (including superconductivity). The book concludes with an introduction to many-body theory, including some applications.

Table of Contents

  • Preface

    Note to the Reader

    Part A

    Chapter 1. Lattice Dynamics

    1.1 Equations of Motion and Their Solution

    1.2 The Reciprocal Lattice and the Brillouin Zone

    1.3 Optical Properties: Classical Theory

    1.4 Quantization of Lattice Vibrations

    1.5 Thermodynamics and the Density of States

    1.6 Scattering of Thermal Neutrons by a Vibrating Crystal Lattice

    1.7 The Mössbauer Effect

    1.8 Lattice Thermal Conductivity

    1.9 Quantum Theory of the Interaction of Lattice Vibrations with Electromagnetic Radiation



    Chapter 2. Phenomenological Theories of Magnetic Order

    2.1 General Description

    2.2 Interaction of Atomic Spins at Large Distances

    2.3 Molecular Field Theory

    2.4 Spin Waves

    2.5 Scattering of Slow Neutrons by Magnetically Ordered Systems

    2.6 The Ising Model

    2.7 The Magnetic Phase Transition



    Chapter 3. Symmetry and Its Consequences

    3.1 Space Groups and Point Groups

    3.2 Irreducible Representations: Point Groups

    3.3 Symmetry with Spin

    3.4 Ions in Crystals

    3.5 Irreducible Representations: Translation Groups and Bloch's Theorem

    3.6 Irreducible Representations: Space Groups

    3.7 Time Reversal Symmetry



    Chapter 4. Energy Bands

    4.1 General Properties of Energy Bands

    4.2 Plane Wave Expansions

    4.3 Orthogonalized Plane Waves

    4.4 Pseudopotential Methods

    4.5 The Tight Binding Method

    4.6 The Cellular Method

    4.7 The Green's Function Method

    4.8 The Augmented Plane Wave Method

    4.9 The Hartree-Fock Method

    4.10 Determination of the Crystal Potential



    Appendices to Part A

    Appendix A. Summation Relations

    Appendix B. Quantization of the Free Electromagnetic Field

    Appendix C. Character Tables and Compatibility Tables

    Appendix D. Second Quantization for a System of Fermions

    Part B

    Chapter 5. Impurities and Alloys

    5.1 Representation Theory

    5.2 Localized Impurity States

    5.3 Impurities with Long Range Potentials

    5.4 Localized Moments

    5.5 Alloys

    5.6 The Kondo Effect



    Chapter 6. External Fields

    6.1 The Steady Electric Field

    6.2 The Steady Magnetic Field

    6.3 The Low Field Diamagnetic Susceptibility

    6.4 The de Haas-Van Alphen Effect

    6.5 Optical Properties

    6.6 Excitons

    6.7 Effect of External Fields on Optical Properties



    Chapter 7. Electrons and Phonons

    7.1 The Electron-Phonon Interaction

    7.2 Transport Phenomena

    7.3 The Hall Effect and Magnetoresistance

    7.4 Electromagnetic Properties of Metals

    7.5 Ultrasonic Attenuation by Electrons

    7.6 Electrical Resistance Due to Lattice Vibrations

    7.7 The Polaron Problem

    7.8 Superconductivity



    Chapter 8. Aspects of t h e Electron-Electron Interaction

    8.1 Properties of Green's Functions

    8.2 Some Properties of an Electron Gas

    8.3 The Landau Theory of Fermi Liquids

    8.4 Electron Interactions and Magnetic Order

    8.5 Many-Body Effects in Semiconductors



    Author Index for Part A

    Author Index for Part B

    Subject Index

Product details

  • No. of pages: 844
  • Language: English
  • Copyright: © Academic Press 1976
  • Published: June 28, 1976
  • Imprint: Academic Press
  • eBook ISBN: 9780323142250

About the Author

Joseph Callaway

Affiliations and Expertise

Louisiana State University, Baton Rouge

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