Quantum Mechanics For Applied Physics And Engineering

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 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 Arbitrary 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