For upper-level undergraduates and graduate students: an introduction to the fundamentals of quantum mechanics, emphasizing aspects essential to an understanding of solid-state theory. Numerous problems (and selected answers), projects, exercises.
For upper-level undergraduates and graduate students: an introduction to the fundamentals of quantum mechanics, emphasizing those aspects of quantum mechanics and quantum statistics essential to an understanding of solid-state theory. With numerous problems (and selected answers), projects, and exercises.
Includes bibliographical references (p. 414-415) and index.
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 Schrödinger 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 SCHRÖDINGER 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 0ºK between Two Metals Separated by a Rectangular Barrier
5 Tunnel Current at 0ºK 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