Quantum Theory of the Solid State

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

Problems

References

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

Problems

References

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

Problems

References

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

Problems

References

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

Problems

References

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

Problems

References

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

Problems

References

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

Problems

References

Author Index for Part A

Author Index for Part B

Subject Index