Quantum Mechanics for Electrical Engineers (eBook)

Dennis M. Sullivan (Autor)

eBook Download: PDF

2011 | 1. Auflage
448 Seiten
Wiley (Verlag)
978-1-118-16977-3 (ISBN)

Infos

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

Autor

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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 29.11.2011
• Reihe/Serie: IEEE Press Series on Microelectronic Systems
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Schlagworte: Circuit Theory & Design / VLSI / ULSI • Electrical & Electronics Engineering • Elektrotechnik u. Elektronik • Halbleiter • Quantenelektronik • Quantenmechanik • Quantum Electronics • Schaltkreise - Theorie u. Entwurf / VLSI / ULSI • Schaltkreistechnik • semiconductors
• ISBN-10: 1-118-16977-8 / 1118169778
• ISBN-13: 978-1-118-16977-3 / 9781118169773