Engineering Quantum Mechanics E-Book

Doyeol Ahn

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley - IEEE
• Sprache: Englisch

Seitenzahl: 247

Veröffentlichungsjahr: 2011

Beschreibung

There has been growing interest in the model of semiconductor lasers with non-Markovian relaxation. Introducing senior and graduate students and research scientists to quantum mechanics concepts, which are becoming an essential tool in modern engineering, Engineering Quantum Mechanics develops a non-Markovian model for the optical gain of semiconductor, taking into account the rigorous electronic band-structure and the non-Markovian relaxation using the quantum statistical reduced-density operator formalism. Example programs based on Fortran 77 are provided for band-structures of zinc-blende and wurtzite quantum wells.

Leseprobe

Table of Contents

Cover

Title page

Copyright page

Preface

PART I: Fundamentals

1 Basic Quantum Mechanics

1.1 MEASUREMENTS AND PROBABILITY

1.2 DIRAC FORMULATION

1.3 BRIEF DETOUR TO CLASSICAL MECHANICS

1.4 A ROAD TO QUANTUM MECHANICS

1.5 THE UNCERTAINTY PRINCIPLE

1.6 THE HARMONIC OSCILLATOR

1.7 ANGULAR MOMENTUM EIGENSTATES

1.8 QUANTIZATION OF ELECTROMAGNETIC FIELDS

1.9 PERTURBATION THEORY

2 Basic Quantum Statistical Mechanics

2.1 ELEMENTARY STATISTICAL MECHANICS

2.2 SECOND QUANTIZATION

2.3 DENSITY OPERATORS

2.4 THE COHERENT STATE

2.5 THE SQUEEZED STATE

2.6 COHERENT INTERACTIONS BETWEEN ATOMS AND FIELDS

2.7 THE JAYNES–CUMMINGS MODEL

3  Elementary Theory of Electronic Band Structure in Semiconductors

3.1 BLOCH THEOREM AND EFFECTIVE MASS THEORY

3.2 THE LUTTINGER–KOHN HAMILTONIAN

3.3 THE ZINC BLENDE HAMILTONIAN

3.4 THE WURTZITE HAMILTONIAN

3.5 BAND STRUCTURE OF ZINC BLENDE AND WURTZITE SEMICONDUCTORS

3.6 CRYSTAL ORIENTATION EFFECTS ON A ZINC BLENDE HAMILTONIAN

3.7 CRYSTAL ORIENTATION EFFECTS ON A WURTZITE HAMILTONIAN

PART II: Modern Applications

4 Quantum Information Science

4.1 QUANTUM BITS AND TENSOR PRODUCTS

4.2 QUANTUM ENTANGLEMENT

4.3 QUANTUM TELEPORTATION

4.4 EVOLUTION OF THE QUANTUM STATE: QUANTUM INFORMATION PROCESSING

4.5 A MEASURE OF INFORMATION

4.6 QUANTUM BLACK HOLES

APPENDIX A: DERIVATION OF EQUATION (4.82)

APPENDIX B: DERIVATION OF EQUATIONS (4.93) AND (4.106)

5 Modern Semiconductor Laser Theory

5.1 DENSITY OPERATOR DESCRIPTION OF OPTICAL INTERACTIONS

5.2 THE TIME-CONVOLUTIONLESS EQUATION

5.3 THE THEORY OF NON-MARKOVIAN OPTICAL GAIN IN SEMICONDUCTOR LASERS

5.4 OPTICAL GAIN OF A QUANTUM WELL LASER WITH NON-MARKOVIAN RELAXATION AND MANY-BODY EFFECTS

5.5 NUMERICAL METHODS FOR VALENCE BAND STRUCTURE IN NANOSTRUCTURES

5.6 ZINC BLENDE BULK AND QUANTUM WELL STRUCTURES

5.7 WURTZITE BULK AND QUANTUM WELL STRUCTURES

5.8 QUANTUM WIRES AND QUANTUM DOTS

APPENDIX: FORTRAN 77 CODE FOR THE BAND STRUCTURE

Index

Copyright © 2011 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

Ahn, Doyeol.

Engineering Quantum Mechanics/Doyeol Ahn, Seoung-Hwan Park.

p. cm.

Includes bibliographical references and index.

ISBN 978-0-470-10763-8

1. Quantum theory. 2. Stochastic processes. 3. Engineering mathematics. 4. Semiconductors–Electric properties–Mathematical models. I. Park, Seoung-Hwan. II. Title.

QC174.12.A393 2011

620.001'53012–dc22

2010044304

oBook ISBN: 978-1-118-01782-1

ePDF ISBN: 978-1-118-01780-7

ePub ISBN: 978-1-118-01781-4

Preface

Quantum mechanics is becoming more important in applied science and engineering, especially with the recent developments in quantum computing, as well as the rapid progress in optoelectronic devices. This textbook is intended for graduate students and advanced undergraduate students in electrical engineering, physics, and materials science and engineering. It also provides the necessary theoretical background for researchers in optoelectronics or semiconductor devices. In the task of providing advanced instruction for both students and researchers, quantum mechanics presents special difficulties because of its hierarchical structures. The more abstract formalisms and techniques are quite meaningless until one has mastered the earlier stages in classical physics, which most engineering students are lacking.

Quantum mechanics has become an essential tool for modern engineering. This book covers topics such as semiconductors and laser physics, which are traditionally quantum mechanical, as well as relatively new topics in the field, such as quantum computation and quantum information. These fields have seen an explosive growth during the past 10 years, as quantum computing or quantum information processing can have a significant impact on today’s electronics and computations. The essence of quantum computing is the direct usage of the superposition and entanglement of quantum mechanics. The most challenging research topics include the generation and manipulation of quantum entangled systems, developing the fundamental theory of entanglement, decoherence control, and the demonstration of the scalability of quantum information processing.

In laser physics, there has been a growing interest in the model of semiconductor lasers with non-Markovian relaxation partially because of the dissatisfaction with the conventional model for optical gain in predicting the correct gain spectrum and the thermodynamic relations. This is mainly due to the poor convergence properties of the lineshape function, that is, the Lorentzian lineshape, used in the conventional model. In this book, a non-Markovian model for the optical gain of semiconductors is developed, taking into account the rigorous electronic band structure, many-body effects, and the non-Markovian relaxation using the quantum statistical reduced-density operator formalism for an arbitrary driven system coupled to a stochastic reservoir. Example programs based on Fortran 77 will also be provided for band structures of zinc blende quantum wells.

Many-body effects are taken into account within the time-dependent Hartree–Fock. Various semiconductor lasers including strained-layer quantum well lasers and wurtzite GaN blue-green quantum well lasers are discussed.

We thank Professor Shun-Lien Chuang, Doyeol Ahn’s Ph.D. thesis adviser, for extensive enlightening and encouragement over many years. We are also grateful to many colleagues and friends, especially Frank Stern, B. D. Choe, Han Jo Lim, H. S. Min, M. S. Kim, Robert Mann, Tim Ralph, K. S. Seo, Y. S. Cho, and Chancellor Sam Bum Lee. The support of our research by the Korean Ministry of Education, Science and Technology is greatly appreciated. This book would not have been completed without the patience and continued encouragement of our editors at Wiley and above all the encouragement and understanding of Taeyeon Yim and Young-Mee An. Thanks for putting up with us.

Doyeol Ahn

Seoung-Hwan Park