Quantum Mechanics for Electrical Engineers

Name: Quantum Mechanics for Electrical Engineers
Author: Dennis M. Sullivan

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Gebonden, 448 blz. | Engels

John Wiley & Sons | e druk, 2012

ISBN13: 9780470874097

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John Wiley & Sons e druk, 2012 9780470874097

Onderdeel van serie IEEE Press Series on Microelectronic Systems

120,57

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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

Specificaties

ISBN13:9780470874097

Taal:Engels

Bindwijze:gebonden

Aantal pagina's:448

Uitgever:John Wiley & Sons

Serie:IEEE Press Series on Microelectronic Systems

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

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