Half Title -- Title Page -- Copyright -- Contents -- Preface to the second edition -- Preface to the first edition -- 1 Electrons in One-Dimensional Periodic Potentials -- 1.1 The Bloch Theorem for One-Dimensional Periodicity -- 1.2 Energy Levels of a Single Quantum Well and of a Periodic Array of Quantum Wells -- 1.3 Transfer Matrix, Resonant Tunneling, and Energy Bands -- 1.3.1 Transmission and Reflection of Electrons from an Arbitrary Potential -- 1.3.2 Double Barrier and Resonant Tunneling -- 1.3.3 Electron Tunneling through a Periodic Potential -- 1.4 The Tight-Binding Model -- 1.4.1 Expansion in Localized Orbitals -- 1.4.2 Tridiagonal Matrices and Continued Fractions -- 1.5 Plane Waves and Nearly Free-Electron Model -- 1.5.1 Expansion in Plane Waves -- 1.5.2 The Mathieu Potential and the Continued Fraction Solution -- 1.6 Some Dynamical Aspects of Electrons in Band Theory -- Appendix A. Solved Problems and Complements -- Further Reading -- 2 Geometrical Description of Crystals: Direct and Reciprocal Lattices -- 2.1 Simple Lattices and Composite Lattices -- 2.1.1 Periodicity and Bravais Lattices -- 2.1.2 Simple and Composite Crystal Structures -- 2.2 Geometrical Description of Some Crystal Structures -- 2.3 Wigner-Seitz Primitive Cells -- 2.4 Reciprocal Lattices -- 2.4.1 Definitions and Basic Properties -- 2.4.2 Planes and Directions in Bravais Lattices -- 2.5 Brillouin Zones -- 2.6 Translational Symmetry and Quantum Mechanical Aspects -- 2.6.1 Translational Symmetry and Bloch Wavefunctions -- 2.6.2 The Parametric k ·p Hamiltonian -- 2.6.3 Cyclic Boundary Conditions -- 2.6.4 Special k Points for Averaging Over the Brillouin Zone -- 2.7 Density-of-States and Critical Points -- Further Reading -- 3 The Sommerfeld Free-Electron Theory of Metals -- 3.1 Quantum Theory of the Free-Electron Gas.

3.2 Fermi-Dirac Distribution Function and Chemical Potential -- 3.3 Electronic Specific Heat in Metals and Thermodynamic Functions -- 3.4 Thermionic Emission from Metals -- Appendix A. Outline of Statistical Physics and Thermodynamic Relations -- A.1 Microcanonical Ensemble and Thermodynamic Quantities -- A.2 Canonical Ensemble and Thermodynamic Quantities -- A.3 Grand Canonical Ensemble and Thermodynamic Quantities -- Appendix B. Fermi-Dirac and Bose-Einstein Statistics for Independent Particles -- B.1 Fermi-Dirac Statistics of Noninteracting Fermions -- B.2 Bose-Einstein Statistics for Noninteracting Bosons -- Appendix C. Modified Fermi-Dirac Statistics in a Model of Correlation Effects -- Further Reading -- 4 The One-Electron Approximation and Beyond -- 4.1 Introductory Remarks on the Many-Electron Problem -- 4.2 The Hartree Equations -- 4.3 Identical Particles and Determinantal Wavefunctions -- 4.4 Matrix Elements Between Determinantal States -- 4.5 The Hartree-Fock Equations -- 4.5.1 Variational Approach and Hartree-Fock Equations -- 4.5.2 Ground-State Energy, Ionization Energies, and Transition Energies -- 4.5.3 Hartree-Fock Equations and Transition Energies in Closed-Shell Systems -- 4.5.4 Hartree-Fock-Slater and Hartree-Fock-Roothaan Approximations -- 4.6 Overview of Approaches Beyond the One-Electron Approximation -- 4.7 Electronic Properties and Phase Diagram of the Homogeneous Electron Gas -- 4.8 The Density Functional Theory and the Kohn-Sham Equations -- Appendix A. Bielectronic Integrals among Spin Orbitals -- Appendix B. Outline of Second Quantization Formalism for Identical Fermions -- Appendix C. An Integral on the Fermi Sphere -- Further Reading -- 5 Band Theory of Crystals -- 5.1 Basic Assumptions of the Band Theory -- 5.2 The Tight-Binding Method (LCAO Method) -- 5.2.1 Description of the Tight-Binding Method for Simple Lattices.

5.2.2 Description of the Tight-Binding Method for Composite Lattices -- 5.2.3 Illustrative Applications of the Tight-Binding Scheme -- 5.3 The Orthogonalized Plane Wave (OPW) Method -- 5.4 The Pseudopotential Method -- 5.5 The Cellular Method -- 5.6 The Augmented Plane Wave (APW) Method -- 5.7 The Green's Function Method (KKR Method) -- 5.7.1 Scattering Integral Equation for a Generic Potential -- 5.7.2 Scattering Integral Equation for a Periodic Muffin-Tin Potential -- 5.8 Iterative Methods in Electronic Structure Calculations -- 5.8.1 The Lanczos or Recursion Method -- 5.8.2 Modified Lanczos Method for Excited States -- 5.8.3 Renormalization Method for Electronic Systems -- Appendix A. Matrix Elements of the Augmented Plane Wave Method -- Appendix B. Solved Problems and Complements -- Appendix C. Evaluation of the Structure Coefficients of the KKR Method with the Ewald Procedure -- Further Reading -- 6 Electronic Properties of Selected Crystals -- 6.1 Band Structure and Cohesive Energy of Rare-Gas Solids -- 6.1.1 General Features of Band Structure of Rare-Gas Solids -- 6.1.2 Cohesive Energy of Rare-Gas Solids -- 6.2 Electronic Properties of Ionic Crystals -- 6.2.1 Introductory Remarks and Madelung Constant -- 6.2.2 Considerations on Bands and Bonds in Ionic Crystals -- 6.3 Covalent Crystals with Diamond Structure -- 6.4 Band Structures and Fermi Surfaces of Some Metals -- 6.5 Carbon-Based Materials and Electronic Structure of Graphene -- Appendix A. Solved Problems and Complements -- Further Reading -- 7 Excitons, Plasmons, and Dielectric Screening in Crystals -- 7.1 Exciton States in Crystals -- 7.2 Plasmon Excitations in Crystals -- 7.3 Static Dielectric Screening in Metals within the Thomas-Fermi Model -- 7.4 The Longitudinal Dielectric Function within the Linear Response Theory -- 7.5 Dielectric Screening within the Lindhard Model.

7.5.1 Static Dielectric Screening in Simple Metals with the Lindhard Model -- 7.5.2 Dynamic Dielectric Screening in Simple Metals and Plasmon Modes -- 7.6 Quantum Expression of the Longitudinal Dielectric Function in Crystals -- 7.7 Surface Plasmons and Surface Polaritons -- Appendix A. Friedel Sum Rule and Fumi Theorem -- Appendix B. Quantum Expression of the Longitudinal Dielectric Function in Materials with the Linear Response Theory -- Appendix C. Lindhard Dielectric Function for the Free-electron Gas -- Appendix D. Quantum Expression of the Transverse Dielectric Function in Materials with the Linear Response Theory -- Further Reading -- 8 Interacting Electronic-Nuclear Systems and the Adiabatic Principle -- 8.1 Interacting Electronic-Nuclear Systems and Adiabatic Potential-EnergySurfaces -- 8.2 Non-Degenerate Adiabatic Surface and Nuclear Dynamics -- 8.2.1 Classical Nuclear Dynamics of Born-Oppenheimer Systems -- 8.2.2 Quantum Nuclear Dynamics of Born-Oppenheimer Systems -- 8.3 Degenerate Adiabatic Surfaces and Jahn-Teller Systems -- 8.3.1 Degenerate Adiabatic Surfaces and Nuclear Dynamics -- 8.3.2 The Jahn-Teller Effect for Doubly Degenerate Electronic States -- 8.3.3 The Jahn-Teller Effect for Triply Degenerate Electronic States -- 8.4 The Hellmann-Feynman Theorem and Electronic-Nuclear Systems -- 8.4.1 General Considerations on the Hellmann-Feynman Theorem -- 8.4.2 Charge Density and Atomic Forces -- 8.5 Parametric Hamiltonians and Berry Phase -- 8.6 The Berry Phase Theory of the Macroscopic Electric Polarization in Crystals -- Appendix A. Simplified Evaluation of Typical Jahn-Teller andRenner-Teller Matrices -- Appendix B. Solved Problems and Complements -- Further Reading -- 9 Lattice Dynamics of Crystals -- 9.1 Dynamics of Monoatomic One-Dimensional Lattices -- 9.2 Dynamics of Diatomic One-Dimensional Lattices.

9.3 Dynamics of General Three-Dimensional Crystals -- 9.4 Quantum Theory of the Harmonic Crystal -- 9.4.1 Canonical Transformation to Independent Oscillators -- 9.4.2 Quantization of the Elastic Field and Phonons -- 9.5 Lattice Heat Capacity. Einstein and Debye Models -- 9.6 Considerations on Anharmonic Effects and Melting of Solids -- 9.7 Optical Phonons and Polaritons in Polar Crystals -- 9.7.1 General Considerations -- 9.7.2 Lattice Vibrations in Polar Crystals and Polaritons -- 9.7.3 Local Field Effects on Polaritons -- Appendix A. Quantum Theory of the Linear Harmonic Oscillator -- Further Reading -- 10 Scattering of Particles by Crystals -- 10.1 General Considerations -- 10.2 Elastic Scattering of X-rays from Crystals and the Thomson Approximation -- 10.2.1 Elastic Scattering of X-rays and Bragg Diffraction Condition -- 10.2.2 Elastic Scattering of X-rays and Intensity of Diffracted Beams -- 10.2.3 Quantum Theory Analysis of the Thomson Cross-Section -- 10.3 Compton Scattering and Electron Momentum Density -- 10.4 Inelastic Scattering of Particles and Phonons Spectra of Crystals -- 10.5 Quantum Theory of Elastic and Inelastic Scattering of Neutrons -- 10.6 Dynamical Structure Factor for Harmonic Displacements and Debye-Waller Factor -- 10.6.1 Dynamical Structure Factor of a Three-Dimensional Harmonic Oscillator -- 10.6.2 Dynamical Structure Factor of a Three-Dimensional Harmonic Crystal -- 10.7 Mössbauer Effect -- Appendix A. Solved Problems and Complements -- Further Reading -- 11 Optical and Transport Properties of Metals -- 11.1 Macroscopic Theory of Optical Constants in Homogeneous Materials -- 11.2 The Drude Theory of the Optical Properties of Free Carriers -- 11.3 Transport Properties and Boltzmann Equation -- 11.4 Static and Dynamic Conductivity in Metals -- 11.4.1 Static Conductivity with the Boltzmann Equation.

11.4.2 Frequency and Wavevector Dependence of the Conductivity.