References.

I ATOMIC STRUCTURE.

1 The Idea of Crystals.

1.1 Introduction.

1.2 Two-Dimensional Lattices.

1.3 Symmetries.

2 Three-Dimensional Lattices.

2.1 Introduction.

2.2 Monatomic Lattices.

2.3 Compounds.

2.4 Classification of Lattices by Symmetry.

2.5 Symmetries of Lattices with Bases.

2.6 Some Macroscopic Implications of Microscopic Symmetries . . . .

3 Scattering and Structures.

3.1 Introduction.

3.2 Theory of Scattering from Crystals.

3.3 Experimental Methods.

3.4 Further Features of Scattering Experiments.

3.5 Correlation Functions.

4 Surfaces and Interfaces.

4.1 Introduction.

4.2 Geometry of Interfaces.

4.3 Experimental Observation and Creation of Surfaces.

5 Beyond Crystals.

5.1 Introduction.

5.2 Diffusion and Random Variables.

5.3 Alloys.

5.4 Simulations.

5.5 Liquids.

5.6 Glasses.

5.7 Liquid Crystals.

5.8 Polymers.

5.9 Colloids and Diffusing-Wave Scattering.

5.10 Quasicrystals.

5.11 Fullerenes and nanotubes.

II ELECTRONIC STRUCTURE.

6 The Free Fermi Gas and Single Electron Model.

6.1 Introduction.

6.2 Starting Hamiltonian.

6.3 Densities of States.

6.4 Statistical Mechanics of Noninteracting Electrons.

6.5 Sommerfeld Expansion.

7 Non-Interacting Electrons in a Periodic Potential.

7.1 Introduction.

7.2 Translational Symmetry—Bloch's Theorem.

7.3 Rotational Symmetry—Group Representations.

8 Nearly Free and Tightly Bound Electrons.

8.1 Introduction.

8.2 Nearly Free Electrons.

8.3 Brillouin Zones.

8.4 Tightly Bound Electrons.

9 Electron-Electron Interactions.

9.1 Introduction.

9.2 Hartree and Hartree-Fock Equations.

9.3 Density Functional Theory.

9.4 Quantum Monte Carlo.

9.5 Kohn-Sham Equations.

10 Realistic Calculations in Solids.

10.1 Introduction.

10.2 Numerical Methods.

10.3 Definition of Metals, Insulators, and Semiconductors.

10.4 Brief Survey of the Periodic Table.

III MECHANICAL PROPERTIES.

11 Cohesion of Solids.

11.1 Introduction.

11.2 Noble Gases.

11.3 Ionic Crystals.

11.4 Metals.

11.5 Band Structure Energy.

11.6 Hydrogen-Bonded Solids.

11.7 Cohesive Energy from Band Calculations.

11.8 Classical Potentials.

12 Elasticity.

12.1 Introduction.

12.2 Nonlinear Elasticity.

12.3 Linear Elasticity.

12.4 Other Constitutive Laws.

13 Phonons.

13.1 Introduction.

13.2 Vibrations of a Classical Lattice.

13.3 Vibrations of a Quantum-Mechanical Lattice.

13.4 Inelastic Scattering from Phonons.

13.5 The Mössbauer Effect.

14 Dislocations and Cracks.

14.1 Introduction.

14.2 Dislocations.

14.3 Two-Dimensional Dislocations and Hexatic Phases.

14.4 Cracks.

15 Fluid Mechanics.

15.1 Introduction.

15.2 Newtonian Fluids.

15.3 Polymeric Solutions.

15.4 Plasticity.

15.5 Superfluida ⁴He.

IV ELECTRON TRANSPORT.

16 Dynamics of Bloch Electrons.

16.1 Introduction.

16.2 Semiclassical Electron Dynamics.

16.3 Noninteracting Electrons in an Electric Field.

16.4 Semiclassical Equations from Wave Packets.

16.5 Quantizing Semiclassical Dynamics.

17 Transport Phenomena and Fermi Liquid Theory.

17.1 Introduction.

17.2 Boltzmann Equation.

17.3 Transport Symmetries.

17.4 Thermoelectric Phenomena.

17.5 Fermi Liquid Theory.

18 Microscopic Theories of Conduction.

18.1 Introduction.

18.2 Weak Scattering Theory of Conductivity.

18.3 Metal-Insulator Transitions in Disordered Solids.

18.4 Compensated Impurity Scattering and Green's Functions.

18.5 Localization.

18.6 Luttinger Liquids.

19 Electronics.

19.1 Introduction.

19.2 Metal Interfaces.

19.3 Semiconductors.

19.4 Diodes and Transistors.

19.5 Inversion Layers.

V OPTICAL PROPERTIES.

20 Phenomenological Theory.

20.1 Introduction.

20.2 Maxwell's Equations.

20.3 Kramers-Kronig Relations.

20.4 The Kubo-Greenwood Formula.

21 Optical Properties of Semiconductors.

21.1 Introduction.

21.2 Cyclotron Resonance.

21.3 Semiconductor Band Gaps.

21.4 Excitons.

21.5 Optoelectronics.

22 Optical Properties of Insulators.

22.1 Introduction.

22.2 Polarization.

22.3 Optical Modes in Ionic Crystals.

22.4 Point Defects and Color Centers.

23 Optical Properties of Metals and Inelastic Scattering.

23.1 Introduction.

23.2 Metals at Low Frequencies.

23.3 Plasmons.

23.4 Interband Transitions.

23.5 Brillouin and Raman Scattering.

23.6 Photoemission.

VI MAGNETISM.

24 Classical Theories of Magnetism and Ordering.

24.1 Introduction.

24.2 Three Views of Magnetism.

24.3 Magnetic Dipole Moments.

24.4 Mean Field Theory and the Ising Model.

24.5 Other Order-Disorder Transitions.

24.6 Critical Phenomena.

25 Magnetism of Ions and Electrons.

25.1 Introduction.

25.2 Atomic Magnetism.

25.3 Magnetism of the Free-Electron Gas.

25.4 Tightly Bound Electrons in Magnetic Fields.

25.5 Quantum Hall Effect.

26 Quantum Mechanics of Interacting Magnetic Moments.

26.1 Introduction.

26.2 Origin of Ferromagnetism.

26.3 Heisenberg Model.

26.4 Ferromagnetism in Transition Metals.

26.5 Spintronics.

26.6 Kondo Effect.

26.7 Hubbard Model.

27 Superconductivity.

27.1 Introduction.

27.2 Phenomenology of Superconductivity.

27.3 Microscopic Theory of Superconductivity.

APPENDICES.

A Lattice Sums and Fourier Transforms.

A.1 One-Dimensional Sum.

A.2 Area Under Peaks.

A.3 Three-Dimensional Sum.

A.4 Discrete Case.

A.5 Convolution.

A.6 Using the Fast Fourier Transform.

B Variational Techniques.

B.1 Functionals and Functional Derivatives.

B.2 Time-Independent Schrödinger Equation.

B.3 Time-Dependent Schrödinger Equation.

B.4 Method of Steepest Descent.

C Second Quantization.

C.1 Rules.

C.2 Derivations.

Index.

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