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- Title Pages
- Preface
- Part I Introductory Topics
- 1 Elastic Behavior of Solids
- 2 Electric Behavior of Insulators
- 3 Metals and the Drude–Lorentz Model
- 4 Elementary Theories of the Thermal Properties of Solids
- 5 Elementary Theories of Magnetism
- 6 The Non-interacting Fermi Gas
- 7 Elementary Theories of Crystal Bonding
- Part II Crystal Structure and its Determination
- 8 Lattices and Crystal Structures
- 9 X-ray Diffraction
- Part III Electronic Structure of Periodic Solids
- 10 Electrons in a Periodic Solid
- 11 The Nearly Free Electron, OPW, Pseudopotential, and Tight Binding Methods
- 12 The Parameterization of Band Structures: Applications to Semiconductors
- 13 Augmented Plane Wave and Green’s Function Methods*
- Part IV Electron–Electron Interaction
- 14 The Self-consistent Dielectric Function
- 15 Hartree–Fock and Density Functional Theory
- Part V Lattice Dynamics
- 16 Harmonic Lattice Dynamics: Classical and Quantum
- 17 Thermal Expansion, Phonon–Phonon Interactions, and Heat Transport
- Part VI Electron Transport and Conduction Electron Dynamics
- 18 Motion of Electrons and Holes in External Electric and Magnetic Fields
- 19 Electronic Transport Properties Governed by Static Scattering Centers
- 20 Measuring the Electronic Energy Spectrum On and Off the Fermi Surface
- 21 The Interacting System of Metallic Electrons and Phonons
- Part VII Semiconductors
- 22 Homogeneous Semiconductors
- 23 Inhomogeneous Semiconductors
- Part VIII Electric and Magnetic Properties of Insulators
- 24 Electric and Magnetic Susceptibilities
- 25 Piezoelectricity, Pyroelectricity, and Ferroelectricity
- Part IX Magnetism
- 26 Ferromagnetism and Antiferromagnetism
- 27 Dynamic Properties of Magnetic Materials
- 28 Magnetic Resonance28
- Part X Optical Properties
- 29 Optical Responses
- 30 Polaritons, Excitons, and Plasmons
- 31 Behavior Under Intense Illumination: NLO, the e–h Liquid and Excitonic BEC
- Part XI Superconductivity and Superfluidity
- 32 A Phenomenological Theory of Superconductivity: The London Equations
- 33 A Phenomenological Theory of Superconductivity: The Ginzburg–Landau Theory and the Josephson Effects
- 34 The Microscopic Theory of Superconductivity: Cooper Pairing and the Bardeen–Cooper–Schrieffer Theory
- 35 Elementary Excitations and the Thermodynamic Properties of Superconductors
- 36 Superfluid4He
- 37 Landau’s Theory of a Fermi Liquid
- 38 Superfluid3He
- Part XII Disordered Materials
- 39 Alloys
- 40 Defects and Diffusion in Crystalline Solids
- 41 Dislocations and Grain Boundaries
- 42 Quantum Theory of Electrical Transport in Dilute Alloys
- 43 Electrical Transport in Highly Disordered Media: Localization/Interaction Effects
- 44 Magnetic Impurities and their Interactions: The Anderson Model, the Kondo Effect, and the RKKY Interaction
- Part XIII Special Topics
- 45 Strongly Correlated Systems
- 46 High Temperature Superconductors
- 47 Artificially Structured and Patterned Materials; Surfaces and Interfaces
- 48 The Quantum Hall Effects
- 49 Graphene, Carbon Nanotubes, and Fullerenes
- Appendix A The Calculus of Variations
- Appendix B The Symmetry of Many–Particle Wave Functions; The Occupation Number RepresentationB
- Index

# (p.997) Appendix A The Calculus of Variations

# (p.997) Appendix A The Calculus of Variations

- Source:
- The Physics of Solids
- Author(s):
### J. B. Ketterson

- Publisher:
- Oxford University Press

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- Title Pages
- Preface
- Part I Introductory Topics
- 1 Elastic Behavior of Solids
- 2 Electric Behavior of Insulators
- 3 Metals and the Drude–Lorentz Model
- 4 Elementary Theories of the Thermal Properties of Solids
- 5 Elementary Theories of Magnetism
- 6 The Non-interacting Fermi Gas
- 7 Elementary Theories of Crystal Bonding
- Part II Crystal Structure and its Determination
- 8 Lattices and Crystal Structures
- 9 X-ray Diffraction
- Part III Electronic Structure of Periodic Solids
- 10 Electrons in a Periodic Solid
- 11 The Nearly Free Electron, OPW, Pseudopotential, and Tight Binding Methods
- 12 The Parameterization of Band Structures: Applications to Semiconductors
- 13 Augmented Plane Wave and Green’s Function Methods*
- Part IV Electron–Electron Interaction
- 14 The Self-consistent Dielectric Function
- 15 Hartree–Fock and Density Functional Theory
- Part V Lattice Dynamics
- 16 Harmonic Lattice Dynamics: Classical and Quantum
- 17 Thermal Expansion, Phonon–Phonon Interactions, and Heat Transport
- Part VI Electron Transport and Conduction Electron Dynamics
- 18 Motion of Electrons and Holes in External Electric and Magnetic Fields
- 19 Electronic Transport Properties Governed by Static Scattering Centers
- 20 Measuring the Electronic Energy Spectrum On and Off the Fermi Surface
- 21 The Interacting System of Metallic Electrons and Phonons
- Part VII Semiconductors
- 22 Homogeneous Semiconductors
- 23 Inhomogeneous Semiconductors
- Part VIII Electric and Magnetic Properties of Insulators
- 24 Electric and Magnetic Susceptibilities
- 25 Piezoelectricity, Pyroelectricity, and Ferroelectricity
- Part IX Magnetism
- 26 Ferromagnetism and Antiferromagnetism
- 27 Dynamic Properties of Magnetic Materials
- 28 Magnetic Resonance28
- Part X Optical Properties
- 29 Optical Responses
- 30 Polaritons, Excitons, and Plasmons
- 31 Behavior Under Intense Illumination: NLO, the e–h Liquid and Excitonic BEC
- Part XI Superconductivity and Superfluidity
- 32 A Phenomenological Theory of Superconductivity: The London Equations
- 33 A Phenomenological Theory of Superconductivity: The Ginzburg–Landau Theory and the Josephson Effects
- 34 The Microscopic Theory of Superconductivity: Cooper Pairing and the Bardeen–Cooper–Schrieffer Theory
- 35 Elementary Excitations and the Thermodynamic Properties of Superconductors
- 36 Superfluid4He
- 37 Landau’s Theory of a Fermi Liquid
- 38 Superfluid3He
- Part XII Disordered Materials
- 39 Alloys
- 40 Defects and Diffusion in Crystalline Solids
- 41 Dislocations and Grain Boundaries
- 42 Quantum Theory of Electrical Transport in Dilute Alloys
- 43 Electrical Transport in Highly Disordered Media: Localization/Interaction Effects
- 44 Magnetic Impurities and their Interactions: The Anderson Model, the Kondo Effect, and the RKKY Interaction
- Part XIII Special Topics
- 45 Strongly Correlated Systems
- 46 High Temperature Superconductors
- 47 Artificially Structured and Patterned Materials; Surfaces and Interfaces
- 48 The Quantum Hall Effects
- 49 Graphene, Carbon Nanotubes, and Fullerenes
- Appendix A The Calculus of Variations
- Appendix B The Symmetry of Many–Particle Wave Functions; The Occupation Number RepresentationB
- Index