Quantum Mechanics for Applied Physics and Engineering

by Albert T. Fromhold Jr.

Overview

This excellent text, directed to upper-level undergraduates and graduate students in engineering and applied physics, introduces the fundamentals of quantum mechanics, emphasizing those aspects of quantum mechanics and quantum statistics essential to an understanding of solid-state theory. A heavy background in mathematics and physics is not required beyond basic courses in calculus, differential equations, and calculus-based elementary physics.
The first three chapters introduce quantum mechanics (using the Schrödinger equations), quantum statistics, and the free-electron theory of metals. Chapters 4 and 5 deal with the WKB approximation and perturbation theory. Chapters 6 and 7 focus on the periodic potential of a crystalline solid and electronic energy bands.
To increase the effectiveness of the material as a learning aid, all developments are carefully worked out, complete details are given for each of the derivations, and successive derivations are developed on a firm basis provided by the preceding material. Throughout the text, examples from solid-state physics illustrate specific applications and demonstrate the principal results that can be deduced by means of quantum theory. Numerous problems (with selected answers), projects, and exercises have been incorporated to facilitate mastery of the text material.

Product Details

ISBN-13:	9780486164694
Publisher:	Dover Publications
Publication date:	07/26/2012
Series:	Dover Books on Physics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	448
File size:	21 MB
Note:	This product may take a few minutes to download.

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 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