Written by an electrical engineering professor for students and professionals in electrical engineering, Quantum Mechanics for Electrical Engineers focuses on those topics in quantum mechanics that are essential for modern semiconductor theory.
1. Introduction
- 1.1 Why Quantum Mechanics?
- 1.2 Simulation of the One-Dimensional, Time-Dependent Schrödinger Equation
- 1.3 Physical Parameters: The Observables
- 1.4 The Potential V(x)
- 1.5 Propagating through Potential Barriers
- 1.6 Summary
- Exercises
- References
2. Stationary States 27
- 2.1 The Infinite Well
- 2.2 Eigenfunction Decomposition
- 2.3 Periodic Boundary Conditions
- 2.4 Eigenfunctions for Arbitrarily Shaped Potentials
- 2.5 Coupled Wells
- 2.6 Bra-ket Notation
- 2.7 Summary
- Exercises
- References
3. Fourier Theory in Quantum Mechanics
- 3.1 The Fourier Transform
- 3.2 Fourier Analysis and Available States
- 3.3 Uncertainty
- 3.4 Transmission via FFT
- 3.5 Summary
- Exercises
- References
4. Matrix Algebra in Quantum Mechanics
- 4.1 Vector and Matrix Representation
- 4.2 Matrix Representation of the Hamiltonian
- 4.3 The Eigenspace Representation
- 4.4 Formalism
- Appendix: Review of Matrix Algebra
- Exercises
- References
5. A Brief Introduction to Statistical Mechanics
- 5.1 Density of States
- 5.2 Probability Distributions
- 5.3 The Equilibrium Distribution of Electrons and Holes
- 5.4 The Electron Density and the Density Matrix
- Exercises
- References
6. Bands and Subbands
- 6.1 Bands in Semiconductors
- 6.2 The Effective Mass
- 6.3 Modes (Subbands) in Quantum Structures
- Exercises
- References
7. The Schrödinger Equation for Spin-1/2 Fermions
- 7.1 Spin in Fermions
- 7.2 An Electron in a Magnetic Field
- 7.3 A Charged Particle Moving in Combined E and B Fields
- 7.4 The Hartree–Fock Approximation
- Exercises
- References
8. The Green’s Function Formulation
- 8.1 Introduction
- 8.2 The Density Matrix and the Spectral Matrix
- 8.3 The Matrix Version of the Green’s Function
- 8.4 The Self-Energy Matrix
- Exercises
- References
9. Transmission
- 9.1 The Single-Energy Channel
- 9.2 Current Flow
- 9.3 The Transmission Matrix
- 9.4 Conductance
- 9.5 Büttiker Probes
- 9.6 A Simulation Example
- Exercises
- References
10. Approximation Methods
- 10.1 The Variational Method
- 10.2 Nondegenerate Perturbation Theory
- 10.3 Degenerate Perturbation Theory
- 10.4 Time-Dependent Perturbation Theory
- Exercises
- References
11. The Harmonic Oscillator
- 11.1 The Harmonic Oscillator in One Dimension
- 11.2 The Coherent State of the Harmonic Oscillator
- 11.3 The Two-Dimensional Harmonic Oscillator
- Exercises
- References
12. Finding Eigenfunctions Using Time-Domain Simulation
- 12.1 Finding the Eigenenergies and Eigenfunctions in One Dimension
- 12.2 Finding the Eigenfunctions of Two-Dimensional Structures
- 12.3 Finding a Complete Set of Eigenfunctions
- Exercises
- References
Appendices
- Appendix A. Important Constants and Units
- Appendix B. Fourier Analysis and the Fast Fourier Transform (FFT)
- Appendix C. An Introduction to the Green’s Function Method
- Appendix D. Listings of the Programs Used in this Book
Index
Quantum Mechanics for Electrical Engineers begins with an introduction to the field, explaining why classical physics fails when dealing with very small particles and small dimensions. Next, the author presents a variety of topics in quantum mechanics, including: - The Schrödinger equation.
- Fourier theory in quantum mechanics.
- Matrix theory in quantum mechanics.
- An introduction to statistical mechanics.
- Transport in semiconductors.
Because this book is written for electrical engineers, the explanations of quantum mechanics are rooted in mathematics such as Fourier theory and matrix theory that are familiar to all electrical engineers. Beginning with the first chapter, the author employs simple MATLAB® computer programs to illustrate key principles. These computer programs can be easily copied and used by readers to become more familiar with the material. They can also be used to perform the exercises at the end of each chapter.
Quantum Mechanics for Electrical Engineers is recommended for upper-level undergraduates and graduate students as well as professional electrical engineers who want to understand the semiconductors of today and the future.
About the Author
- Dennis M. Sullivan is Professor of Electrical and Computer Engineering at the University of Idaho as well as an award-winning author and researcher. In 1997, Dr. Sullivan's paper "Z Transform Theory and FDTD Method" won the IEEE Antennas and Propagation Society's R. P. W. King Award for the Best Paper by a Young Investigator. He is the author of Electromagnetic Simulation Using the FDTD Method.
Product Details
- Hardcover: 448 pages
- Publisher: Wiley-IEEE Press; 1 edition (January 24, 2012)
- Language: English
- ISBN-10: 0470874090
- ISBN-13: 978-0470874097
List Price: $89.95