Quantum Mechanics for Electrical Engineers (Ieee Press Series on Microelectronic Systems)

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Quantum Mechanics for Electrical Engineers (Ieee Press Series on Microelectronic Systems)

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  • 製本 Hardcover:ハードカバー版/ページ数 429 p.
  • 言語 ENG
  • 商品コード 9780470874097
  • DDC分類 530.120246213

Full Description


The main topic of this book is quantum mechanics, as the title indicates. It specifically targets those topics within quantum mechanics that are needed to understand modern semiconductor theory. It begins with the motivation for quantum mechanics and why classical physics fails when dealing with very small particles and small dimensions. Two key features make this book different from others on quantum mechanics, even those usually intended for engineers: First, after a brief introduction, much of the development is through Fourier theory, a topic that is at the heart of most electrical engineering theory. In this manner, the explanation of the quantum mechanics is rooted in the mathematics familiar to every electrical engineer. Secondly, beginning with the first chapter, simple computer programs in MATLAB are used to illustrate the principles. The programs can easily be copied and used by the reader to do the exercises at the end of the chapters or to just become more familiar with the material. Many of the figures in this book have a title across the top. This title is the name of the MATLAB program that was used to generate that figure. These programs are available to the reader.Appendix D lists all the programs, and they are also downloadable at http://booksupport.wiley.com

Table of Contents

Preface                                            xiii
Acknowledgments xv
About the Author xvii
1 Introduction 1 (26)
1.1 Why Quantum Mechanics? 1 (6)
1.1.1 Photoelectric Effect 1 (1)
1.1.2 Wave-Particle Duality 2 (1)
1.1.3 Energy Equations 3 (2)
1.1.4 The Schrodinger Equation 5 (2)
1.2 Simulation of the One-Dimensional, 7 (7)
Time-Dependent Schrodinger Equation
1.2.1 Propagation of a Particle in Free 8 (3)
Space
1.2.2 Propagation of a Particle 11 (3)
Interacting with a Potential
1.3 Physical Parameters: The Observables 14 (3)
1.4 The Potential V(x) 17 (3)
1.4.1 The Conduction Band of a 17 (1)
Semiconductor
1.4.2 A Particle in an Electric Field 17 (3)
1.5 Propagating through Potential Barriers 20 (3)
1.6 Summary 23 (1)
Exercises 24 (1)
References 25 (2)
2 Stationary States 27 (24)
2.1 The Infinite Well 28 (6)
2.1.1 Eigenstates and Eigenenergies 30 (3)
2.1.2 Quantization 33 (1)
2.2 Eigenfunction Decomposition 34 (4)
2.3 Periodic Boundary Conditions 38 (1)
2.4 Eigenfunctions for Arbitrarily Shaped 39 (2)
Potentials
2.5 Coupled Wells 41 (3)
2.6 Bra-ket Notation 44 (3)
2.7 Summary 47 (1)
Exercises 47 (2)
References 49 (2)
3 Fourier Theory in Quantum Mechanics 51 (20)
3.1 The Fourier Transform 51 (4)
3.2 Fourier Analysis and Available States 55 (4)
3.3 Uncertainty 59 (3)
3.4 Transmission via FFT 62 (4)
3.5 Summary 66 (1)
Exercises 67 (2)
References 69 (2)
4 Matrix Algebra in Quantum Mechanics 71 (20)
4.1 Vector and Matrix Representation 71 (5)
4.1.1 State Variables as Vectors 71 (2)
4.1.2 Operators as Matrices 73 (3)
4.2 Matrix Representation of the 76 (5)
Hamiltonian
4.2.1 Finding the Eigenvalues and 77 (1)
Eigenvectors of a Matrix
4.2.2 A Well with Periodic Boundary 77 (3)
Conditions
4.2.3 The Harmonic Oscillator 80 (1)
4.3 The Eigenspace Representation 81 (2)
4.4 Formalism 83 (2)
4.4.1 Hermitian Operators 83 (1)
4.4.2 Function Spaces 84 (1)
Appendix: Review of Matrix Algebra 85 (3)
Exercises 88 (2)
References 90 (1)
5 A Brief Introduction to Statistical 91 (24)
Mechanics
5.1 Density of States 91 (7)
5.1.1 One-Dimensional Density of States 92 (2)
5.1.2 Two-Dimensional Density of States 94 (2)
5.1.3 Three-Dimensional Density of 96 (1)
States
5.1.4 The Density of States in the 97 (1)
Conduction Band of a Semiconductor
5.2 Probability Distributions 98 (9)
5.2.1 Fermions versus Classical 98 (1)
Particles
5.2.2 Probability Distributions as a 99 (2)
Function of Energy
5.2.3 Distribution of Fermion Balls 101 (4)
5.2.4 Particles in the One-Dimensional 105 (1)
Infinite Well
5.2.5 Boltzmann Approximation 106 (1)
5.3 The Equilibrium Distribution of 107 (3)
Electrons and Holes
5.4 The Electron Density and the Density 110 (3)
Matrix
5.4.1 The Density Matrix 111 (2)
Exercises 113 (1)
References 114 (1)
6 Bands and Subbands 115 (16)
6.1 Bands in Semiconductors 115 (3)
6.2 The Effective Mass 118 (5)
6.3 Modes (Subbands) in Quantum Structures 123 (5)
Exercises 128 (1)
References 129 (2)
7 The Schrodinger Equation for Spin-1/2 131 (28)
Fermions
7.1 Spin in Fermions 131 (11)
7.1.1 Spinors in Three Dimensions 132 (3)
7.1.2 The Pauli Spin Matrices 135 (1)
7.1.3 Simulation of Spin 136 (6)
7.2 An Electron in a Magnetic Field 142 (4)
7.3 A Charged Particle Moving in Combined 146 (2)
E and B Fields
7.4 The Hartree-Fock Approximation 148 (7)
7.4.1 The Hartree Term 148 (5)
7.4.2 The Fock Term 153 (2)
Exercises 155 (2)
References 157 (2)
8 The Green's Function Formulation 159 (18)
8.1 Introduction 160 (1)
8.2 The Density Matrix and the Spectral 161 (3)
Matrix
8.3 The Matrix Version of the Green's 164 (5)
Function
8.3.1 Eigenfunction Representation of 165 (2)
Green's Function
8.3.2 Real Space Representation of 167 (2)
Green's Function
8.4 The Self-Energy Matrix 169 (7)
8.4.1 An Electric Field across the 174 (1)
Channel
8.4.2 A Short Discussion on Contacts 175 (1)
Exercises 176 (1)
References 176 (1)
9 Transmission 177 (22)
9.1 The Single-Energy Channel 177 (2)
9.2 Current Flow 179 (2)
9.3 The Transmission Matrix 181 (8)
9.3.1 Flow into the Channel 183 (1)
9.3.2 Flow out of the Channel 184 (1)
9.3.3 Transmission 185 (1)
9.3.4 Determining Current Flow 186 (3)
9.4 Conductance 189 (2)
9.5 Buttiker Probes 191 (3)
9.6 A Simulation Example 194 (2)
Exercises 196 (1)
References 197 (2)
10 Approximation Methods 199 (28)
10.1 The Variational Method 199 (3)
10.2 Nondegenerate Perturbation Theory 202 (4)
10.2.1 First-Order Corrections 203 (3)
10.2.2 Second-Order Corrections 206 (1)
10.3 Degenerate Perturbation Theory 206 (3)
10.4 Time-Dependent Perturbation Theory 209 (14)
10.4.1 An Electric Field Added to an 212 (1)
Infinite Well
10.4.2 Sinusoidal Perturbations 213 (2)
10.4.3 Absorption, Emission, and 215 (1)
Stimulated Emission
10.4.4 Calculation of Sinusoidal 216 (5)
Perturbations Using Fourier Theory
10.4.5 Fermi's Golden Rule 221 (2)
Exercises 223 (2)
References 225 (2)
11 The Harmonic Oscillator 227 (18)
11.1 The Harmonic Oscillator in One 227 (6)
Dimension
11.1.1 Illustration of the Harmonic 232 (1)
Oscillator Eigenfunctions
11.1.2 Compatible Observables 233 (1)
11.2 The Coherent State of the Harmonic 233 (5)
Oscillator
11.2.1 The Superposition of Two 234 (1)
Eigentates in an Infinite Well
11.2.2 The Superposition of Four 235 (1)
Eigenstates in a Harmonic Oscillator
11.2.3 The Coherent State 236 (2)
11.3 The Two-Dimensional Harmonic 238 (6)
Oscillator
11.3.1 The Simulation of a Quantum Dot 238 (6)
Exercises 244 (1)
References 244 (1)
12 Finding Eigenfunctions Using Time-Domain 245 (16)
Simulation
12.1 Finding the Eigenenergies and 245 (4)
Eigenfunctions in One Dimension
12.1.1 Finding the Eigenfunctions 248 (1)
12.2 Finding the Eigenfunctions of 249 (8)
Two-Dimensional Structures
12.2.1 Finding the Eigenfunctions in an 252 (5)
Irregular Structure
12.3 Finding a Complete Set of 257 (2)
Eigenfunctions
Exercises 259 (1)
References 259 (2)
Appendix A Important Constants and Units 261 (4)
Appendix B Fourier Analysis and the Fast 265 (8)
Fourier Transform (FFT)
B.1 The Structure of the FFT 265 (2)
B.2 Windowing 267 (3)
B.3 FFT of the State Variable 270 (1)
Exercises 271 (1)
References 271 (2)
Appendix C An Introduction to the Green's 273 (8)
Function Method
C.1 A One-Dimensional Electromagnetic 275 (4)
Cavity
Exercises 279 (1)
References 279 (2)
Appendix D Listings of the Programs Used in 281 (138)
this Book
D.1 Chapter 1 281 (3)
D.2 Chapter 2 284 (11)
D.3 Chapter 3 295 (14)
D.4 Chapter 4 309 (3)
D.5 Chapter 5 312 (2)
D.6 Chapter 6 314 (9)
D.7 Chapter 7 323 (13)
D.8 Chapter 8 336 (9)
D.9 Chapter 9 345 (11)
D.10 Chapter 10 356 (22)
D.11 Chapter 11 378 (17)
D.12 Chapter 12 395 (20)
D.13 Appendix B 415 (4)
Index 419