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This page intentionally left blank Fundamentals of Quantum Mechanics For Solid State Electronics and Optics C. L. Tang Cornell University, Ithaca, NY Cambridge University Press Cambridge New York Melbourne Madrid Cape Town Singapore São Paulo Published in the United States of America by Cambridge University Press, New York www.cambridge.org © Cambridge University Press 2005 ISBN-13 978-0-521-82952-6 (hardback) ISBN-10 0-521-82952-6 (hardback) ISBN-13 978-0-511-12595-9 (eBook - NetLibrary) ISBN-10 0-511-12595-x (eBook - NetLibrary) Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. To Louise Contents Preface 1 Classical mechanics vs. quantum mechanics 2 Basic postulates and mathematical tools 3 Wave particle duality and de Broglie waves 4 Particles at boundaries, potential steps, barriers, and in quantum wells 5 The harmonic oscillator and photons 6 The hydrogen atom 7 Multi-electron ions and the periodic table 8 Interaction of atoms with electromagnetic radiation 9 Simple molecular orbitals and crystalline structures 10 Electronic properties of semiconductors and the p-n junction 11 The density matrix and the quantum mechanic Boltzmann equation Preface Quantum mechanics has evolved from a subject of study in pure physics to one with a vast range of applications in many diverse fields. Some of its most important applications are in modern solid state electronics and optics. As such, it is now a part of the required undergraduate curriculum of more and more electrical engineering, materials science, and applied physics schools. This book is based on the lecture notes that I have developed over the years teaching introductory quantum mechanics to students at the senior first year graduate school level whose interest is primarily in applications in solid state electronics and modern optics. There are many excellent introductory text books on quantum mechanics for students majoring in physics or chemistry that emphasize atomic and nuclear physics for the former and molecular and chemical physics for the latter. Often, the approach is to begin from a historic perspective, recounting some of the experimental observations that could not be explained on the basis of the principles of classical mechanics and electrodynamics, followed by descriptions of various early attempts at developing a set of new principles that could explain these 'anomalies.' It is a good way to show the students the historical thinking that led to the discovery and formulation of the basic principles of quantum mechanics. This might have been a reasonable approach in the first half of the twentieth century when it was an interesting story to be told and people still needed to be convinced of its validity and utility. Most students today know that quantum theory is now well established and important. What they want to know is not how to reinvent quantum mechanics, but what the basic principles are concisely and how they are used in applications in atomic, molecular, and solid state physics. For electronics, materials science, and applied physics students in particular, they need to see, above all, how quantum mechanics forms the foundations of modern semiconductor electronics and optics. To meet this need is then the primary goal of this introductory text reference book, for such students and for those who did not have any quantum mechanics in their earlier days as an undergraduate student but wish now to learn the subject on their own. This book is not encyclopedic in nature but is focused on the key concepts and results. Hopefully it makes sense pedagogically. As a textbook, it is conceptually and mathematically self-contained in the sense that all the results are derived, or derivable, from first principles, based on the material presented in the book in a logical order without excessive reliance on reference sources. The emphasis is on concise physical explanations, complemented by rigorous mathematical demonstrations, of how things work and why they work the way they do. Ключевые слова: e, r, o