This book contains advanced subjects in solid state physics with emphasis on the theoretical exposition of various physical phenomena in solids using quantum theory, hence entitled """"A modern course in the quantum theory of solids"""". The use of the adjective """"modern"""" in the title is to reflect the fact that some of the new developments in condensed matter physics have been included in the book. The new developments contained in the book are mainly in experimental methods (inelastic neutron scattering and photoemission spectroscopy), in magnetic properties of solids (the itinerant magnetism, the superexchange, the Hubbard model, and giant and colossal magnetoresistance), and in optical properties of solids (Raman scattering). Besides the new developments, the Green's function method used in many-body physics and the strong-coupling theory of superconductivity are also expounded in great detail.

Description-Table Of Contents

1. Lattice dynamics. 1.1. Born-Oppenheimer approximation. 1.2. Lattice potential energy and harmonic approximation. 1.3. Normal modes of a three-dimensional crystal with a multi-atom basis. 1.4. Classical theory of the lattice specific heat. 1.5. Quantization of lattice vibrations. 1.6. Phonon density of states. 1.7. Lattice specific heat of solids. 1.8. Debye model. 1.9. Einstein model. 1.10. Effect of thermal expansion on phonon frequencies. 1.11. Specific heat of a metal. Problems -- 2. Determination of phonon dispersion relations. 2.1. Experimental techniques. 2.2. Description of neutron scattering. 2.3. Double differential cross-section. 2.4. Elastic scattering. 2.5. Inelastic scattering. Problems -- 3. Elementary theory of energy bands. 3.1. Development of computational methods for band structures. 3.2. Fundamental problem in an energy band theory. 3.3. Hartree-Fock method. 3.4. Plane-wave method. 3.5. k•p method. 3.6. Augmented-plane-wave method. 3.7. Linearized-augmented-plane-wave method. 3.8. Linear-muffin-tin-orbitals method. 3.9. KKR method. 3.10. Orthogonalized-plane-wave method. 3.11. Tight-binding method. Problems -- 4. Determination of electronic band structures. 4.1. Interaction of electrons with electromagnetic fields. 4.2. De Haas-van Alphen effect. 4.3. Photoemission spectroscopy. Problems -- 5. Electron-phonon interaction. 5.1. Electron-phonon interaction Hamiltonian. 5.2. Electron-phonon interaction in metals. 5.3. Polarons. 5.4. Green's functions at zero temperature. 5.5. Green's functions at finite temperatures. Problems -- 6. Transport properties of solids. 6.1. Boltzmann equation. 6.2. Electrical conductivity of nearly free electrons. 6.3. Mechanisms for electron scattering. 6.4. Thermal conductivity of metals. 6.5. Linear response theory. 6.6. Kubo formula for electrical conductivity. 6.7. Kubo-Greenwood formula. Problems -- 7. Magnetic properties of solids. 7.1. Classification of magnetic solids. 7.2. Fundamental quantities related to magnetism. 7.3. Diamagnetism and paramagnetism of insulators. 7.4. Magnetism of conduction electrons. 7.5. Exchange interaction and Heisenberg model. 7.6. Ferromagnetism. 7.7. Magnetic domains in ferromagnets. 7.8. Ferrimagnetism. 7.9. Antiferromagnetism. 7.10. Itinerant magnetism. 7.11. Indirect exchange interactions. 7.12. Giant magnetoresistance. Problems -- 8. Optical properties of solids. 8.1. Description of the optical properties. 8.2. Optical properties of free electrons. 8.3. Optical properties of alkali metals. 8.4. Optical properties of transition metals. 8.5. Optical properties of insulators. 8.6. Absorption of light. 8.7. Optical properties of semiconductors. 8.8. Raman scattering. 8.9. Polaritons. Problems -- 9. Superconductivity. 9.1. Properties of a superconductor. 9.2. Phenomenological theories. 9.3. BCS theory of superconductivity. 9.4. Electron tunneling. 9.5. Josephson effect. 9.6. Strong-coupling theory. Problems.