Table of Contents

Preface Acknowledgments PART I ELEMENTARY QUANTUM THEORY Chapter 1 An Introduction to Quantum Mechanics 1 Wave-Particle Duality 2 Classical Wave Motion 3 Periodic Boundary Conditions and Complex Fourier Components 4 Fourier Series and Fourier Integrals 5 Wave Nature of Particles 6 Development of the Time-Dependent and Time-Independent Schrodinger Wave Equations 7 Wave-Packet Solutions and the Uncertainty Relation 8 Expectation Values for Quantum-Mechanical Operators 9 Probability Current Density 10 Energy Levels and Density of States 11 Reflection and Transmission Coefficients for a Particle Beam at a Potential-Energy Step Discontinuity and at a Rectangular Barrier 12 Bound-State Problems Problems Answers to Multiple Choice Problems PART II QUANTUM STATISTICS OF MANY-PARTICLE SYSTEMS; FORMULATION OF THE FREE-ELECTRON MODEL FOR METALS Chapter 2 Many-Particle Systems and Quantum Statistics 1 Wave Functions for a Many-Particle System 2 Statistics for a Many-Particle System Problems Chapter 3 Free-Electron Model and the Boltzmann Equation 1 Free-Electron Gas in Three Dimensions 2 Electronic Specific Heat 3 Electrical Conductivity and the Derivation of Ohm's Law 4 Thermal Electron Emission from Metals 5 General Method for Evaluating Statistical Quantities Involving Fermi-Dirac Statistics 6 The Temperature Dependence of the Fermi Energy and Other Applications of the General Approximation Technique 7 The Boltzmann Equation Problems PART III APPROXIMATION TECHNIQUES FOR THE SCHRODINGER EQUATION Chapter 4 The WKB Approximation and Electron Tunneling 1 Development of the WKB Approximation 2 Application of the WKB Technique to Barrier Penetration 3 Tunneling in Metal-Insulator-Metal Structures 4 Tunnel Current at 0 * K between Two Metals Separated by a Rectangular Barrier 5 Tunnel Current at 0 * K for Barriers of Arbitrary Shape 6 Temperature Dependence of the Electron Tunnel Current 7 Applications of Electron Tunneling "Chapter 5 Perturbation Theory, Diffraction of Valence Electrons, and the Nearly-Free-Electron Model" 1 Stationary-State Perturbation Theory 2 Elementary Treatment of Diagonalization 3 Higher-Order Perturbations and Applications 4 Degenerate Case for Second-Order Treatment 5 Removal of Degeneracy in Second Order 6 Time-Dependent Perturbation Theory 7 Example: Harmonic Perturbation 8 Example: Constant Perturbation in First Order 9 Example: Constant Perturbation in Second Order 10 Transition Probability and Fermi's Golden Rule 11 Differential Cross Section for Scattering 12 Diffraction of Electrons by the Periodic Potential of a Crystal 13 Diffraction of Conduction Electrons and the Nearly-Free-Electron Model 14 Differential Scattering Cross Section for Plane-Wave States and a Coulomb Potential Problems PART IV ENERGY BANDS IN CRYSTALS Chapter 6 The Periodicity of Crystalline Solids 1 Generalities 2 Unit Cells and Bravais Lattices 3 Miller Indices and Crystal Directions 4 Some Specific Crystal Structures 5 Crystal Bonding 6 The Reciprocal Lattice: Fourier Space for Arbitrary Functions That Have the Lattice Periodicity 7 Wigner-Seitz Cell 8 First Brillouin Zone 9 Higher Brillouin Zones Problems Chapter 7 Bloch's Theorem and Energy Bands for a Periodic Potential 1 Fourier Series Expansions for Arbitary Functions of Position within the Crystal 2 The Periodic Potential Characteristic of the Perfect Monocrystal 3 The Hamiltonian for an Electron in a Periodic Potential 4 Fourier Series Derivation of Bloch's Theorem 5 Properties of Bloch Functions 6 Correspondence with the Free-Electron Model 7 Additional Properties of Bloch Functions 8 Energy Bands from the Viewpoint of the One-Electron Atomic Levels 9 "Energy Gaps and Energy Bands: Insulators, Semiconductors, and Metals" Problems "Appendix Physical Constants: Symbols, Units, and Values" References Index