Introduction to Solid-State Theory

Introduction to Solid-State Theory is a textbook for graduate students of physics and materials science. It also provides the theoretical background needed by physicists doing research in pure solid-state physics and its applications to electrical engineering. The fundamentals of solid-state theory are based on a description by delocalized and localized states and - within the concept of delocalized states - by elementary excitations. The development of solid-state theory within the last ten years has shown that by a systematic introduction of these concepts, large parts of the theory can be described in a unified way. This form of description gives a "pictorial" formulation of many elementary processes in solids, which facilitates their understanding.   

1. Fundamentals.- 1.1 Introduction.- 1.2 The Basic Hamiltonian.- 1.3 The Hartree-Fock Approximation.- 2. The One-Electron Approximation.- 2.1 The Electron Gas Without Interaction.- 2.2 Electrons in a Periodic Potential.- 2.2.3 The Schrödinger Equation for Electrons in a Periodic Potential.- 2.2.5 Consequences of Translational Invariance.- 2.2.7 Wannier Functions, LCAO Approximation.- 3. Elementary Excitations.- 3.1 The Interacting Electron Gas: Quasi-Electrons and Plasmons.- 3.2 Electron-Hole Interaction in Semiconductors and Insulators: Excitons.- 3.3 Ion-Ion Interaction: Phonons.- 3.4 Spin-Spin Interaction: Magnons.- 4. Electron-Phonon Interaction: Transport Phenomena.- 4.1 The Interaction Processes.- 4.2 The Boltzmann Equation.- 4.2 Boltzmann Equations for the Electron and Phonon Systems.- 4.3 Formal Transport Theory.- 4.4 Transport in Metals and Semiconductors.- 5. Electron-Electron Interaction by Exchange of Virtual Phonons: Superconductivity.- 5.1 Introduction.- 5.2 Cooper Pairs.- 5.3 The Ground State of the Superconducting Electron Gas.- 5.4 Excited States.- 5.5 Comparison with Experiment.- 5.6 Thc Meissner-Ochsenfeld Effect.- 5.7 Further Theoretical Concepts.- 6. Interaction with Photons: Optics.- 6.1 Fundamentals.- 6.2 Electron-Photon Interaction.- 6.3 Phonon-Photon Interaction.- 7. Phonon-Phonon Interaction: Thermal Properties.- 7.1 Introduction.- 7.2 Frequency Shift and Lifetime of Phonons.- 7.3 The Anharmonic Contributions to the Free Energy, Thermal Expansion.- 7.4 The Thermal Conductivity of the Lattice.- 8. Local Description of Solid-State Properties.- 8.1 Localized and Extended States.- 8.2 The Chemical Bond.- 8.3 Local Versus Nonlocal Description in Unperturbed Lattices.- 9. Localized States.- 9.1 Point Imperfections.- 9.2 Localized States andElementary Excitations at Surfaces.- 10. Disorder.- 10.1 Localized States in Disordered Lattices.- 10.2 Transport in Disordered Lattices.- 10.2 The Hopping Probability.- Appendix: The Occupation Number Representation.- Problems to Chapters 1–9.