Quantum Mechanics for Electrical Engineers

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 booksupport.wiley.com

The main topic of this book is quantum mechanics, as the titleindicates. It specifically targets those topics within quantummechanics that are needed to understand modern semiconductortheory. It begins with the motivation for quantum mechanics and whyclassical physics fails when dealing with very small particles andsmall dimensions. Two key features make this book different fromothers on quantum mechanics, even those usually intended forengineers: First, after a brief introduction, much of thedevelopment is through Fourier theory, a topic that is at the heartof most electrical engineering theory. In this manner, theexplanation of the quantum mechanics is rooted in the mathematicsfamiliar to every electrical engineer. Secondly, beginning with thefirst chapter, simple computer programs in MATLAB are used toillustrate the principles. The programs can easily be copied andused by the reader to do the exercises at the end of the chaptersor 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 togenerate that figure. These programs are available to the reader.Appendix D lists all the programs, and they are also downloadableat href="booksupport.wiley.com/">booksupport.wiley.com

1. Introduction1.1 Why Quantum Mechanics1.2 Simulation of the One-Dimensional, Time-Dependent Schrödinger Equation1.3 Physical Parameters-the Observables1.4 The Potential V(X)1.5 Propagating Through Potential Barriers1.6 Summary2. Stationary States2.1 The Infinite Well2.2 Eigenfunction Decomposition2.3 Periodic Boundary Conditions2.4 Eigenfunctions for Arbitrarily Shaped Potentials2.5 Coupled Wells2.6 Bra-ket Notation2.7 Summary.3. Fourier Theory in Quantum Mechanics3.1 The Fourier Transform3.2 Fourier Analysis and Available States3.3 Uncertainty3.4 Transmission via FFT3.5 Summary4. Matrix Algebra in Quantum Mechanics4.1 Vector and Matrix Representation4.2 Matrix Representation of the Hamiltonian4.3 The Eigenspace Representation4.4 Formalism5. Statistical Mechanics5.1 Density of States5.2 Probability Distributions5.3 The Equilibrium Distribution of Electrons and Holes5.4 The Electron Density and the Density Matrix6. Bands and Subbands6.1 Bands in Semiconductors6.2 The Effective Mass6.3 Modes (Subbands) in Quantum Structures7. The Schrödinger Equation for Spin-1.2 Fermions7.1 Spin in Fermions7.2 An Electron in a Magnetic Field7.3 A Charged Particle Moving in Combined E and B fields7.4 The Hartree-Fock Approximation8. Green's Functions Formulation8.1 Introduction8.2 The Density Matrix and the Spectral Matrix8.3 The Matrix Version of the Green's Function8.4 The Self-Energy Matrix9. Transmission9.1 The Single-Energy Channel9.2 Current Flow9.3 The Transmission Matrix9.4 Conductance9.5 Büttiker probes9.6 A Simulation Example10. Approximation Methods10.1 The Variational Method10.2 Non-Degenerate Perturbation Theory10.3 Degenerate Perturbation Theory10.4 Time-Dependent Perturbation Theory11. The Harmonic Oscillator11.1 The Harmonic Oscillator in One Dimension11.2 The Coherent State of the Harmonic Oscillator11.3 The Two-Dimensional Harmonic Oscillator12. Finding Eigenfunctions Using Time-Domain Simulation12.1 Finding the Eigenenergies and Eigenfunctions in One-Dimension12.2 Finding the Eigenfunctions of Two-Dimensional Structures12.3 Finding a Complete set of EigenfunctionsAppendix A. Important Constants and UnitsAppendix B. Fourier Analysis and the Fast Fourier Transform (FFT)Appendix C. An Introduction to the Green's FunctionAppendix D. Listing of Computer Programs