Sullivan Quantum Mechanics for Electrical Engineers

1. Auflage 2011
ISBN: 978-1-118-16979-7
Verlag: John Wiley & Sons
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 448 Seiten, E-Book

Reihe: IEEE Press Series on Microelectronic Systems

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 http://booksupport.wiley.com

Autoren/Hrsg.

Sullivan, Dennis M.

Inhaltsverzeichnis

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
2. Stationary States
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.
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
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
5. 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
6. Bands and Subbands
6.1 Bands in Semiconductors
6.2 The Effective Mass
6.3 Modes (Subbands) in Quantum Structures
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
8. Green's Functions 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
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
10. Approximation Methods
10.1 The Variational Method
10.2 Non-Degenerate Perturbation Theory
10.3 Degenerate Perturbation Theory
10.4 Time-Dependent Perturbation Theory
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
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
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
Appendix D. Listing of Computer Programs

Über Autor(innen)

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.