Modern Physics for Scientists and Engineers Modern Physics for Scientists and Engineers Second Edition John C. Morrison Physics Department, University of Louisville, Louisville, KY, USA AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Academic Press is an imprint of Elsevier www.com Academic Press is an imprint of Elsevier 32 Jamestown Road, London NW1 7BY, UK 525 B Street, Suite 1800, San Diego, CA 92101-4495, USA 225 Wyman Street, Waltham, MA 02451, USA The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK Copyright © 2015, 2010 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
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Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. Library of Congress Cataloging-in-Publication Data A catalogue record for this book is available from the Library of Congress British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-12-800734-1 For information on all Academic Press Publications visit our Website at www.com Dedication This book is dedicated to the scientists and mathematicians in the Holy Lands who are striving for peace in a spiritually and culturally rich part of the world.com Online applets are available to solve realistic problems in atomic and condensed matter physics.
You can find the applets at: http://booksite.com/Morrison/physics/ www.com Preface Modern Physics for Scientists and Engineers presents the ideas that have shaped modern physics and provides an introduction to current research in the different fields of physics. Intended as the text for a first course in modern physics following an introductory course in physics with calculus, the book begins with a brief and focused account of historical events leading to the formulation of modern quantum theory, while ensuing chapters go deeper into the underlying physics. This book helps prepare engineering students for the upper division courses on devices they will later take and provides engineering and physics majors an overview of contemporary physics. The course in modern physics is the last course in physics most engineering students will ever take.
For this reason, this book covers a few topics that are ordinarily taught at the junior/senior level. I include these advanced topics because they are relevant and interesting to engineering students and because these topics would ordinarily be unavailable to them. Topics such as Bloch’s theorem, heterostructures, quantum wells and barriers, and a phenomenological description of semiconductor lasers help to give engineering students the physics background they need for the courses they will later take on semiconductor devices, while subjects like the Hartree-Fock theory, Bose-Einstein condensation, the relativistic Dirac equation, and particle physics help students appreciate the range and scope of contemporary physics. This course helps physics majors by giving them a substantial introduction to quantum theory and to the various fields of modern physics.
The books I have used to prepare later chapters of this book are just the books used in upper-division courses in the various fields of contemporary physics. THIS NEW EDITION The challenge in preparing this new edition has been to describe the developments that have occurred in physics since the first edition of this book appeared in January 2010. I would like to thank Keith Ellis of the Theory Group at Fermilab for discussing recent developments in particle physics with me and correcting the two new sections I have written on local gauge invariance and the discovery of the Higgs Boson. Thanks are also due to Chris Quigg at Fermilab, Ken Hicks at Ohio University, and Wafaa Khater at Birzeit University.
My writing of the two new sections on graphene and carbon nanotubes was also greatly helped by Fendinand Evers at Karlsruher Institute of Technology and by Gamini Sumanesekera and Shi-Yu Wu at University of Louisville. NEW FEATURES In this new edition of Modern Physics for Scientists and Engineers, I have included a description of simulations from the educational software package PhET developed at the University of Colorado. These simulations, which can be accessed online, enable students to gain an intuitive understanding of how waves interfere with each other and how waves can be combined to form wave packets. The new edition also contains many exercises using the software package MATLAB.
A new appendix on MATLAB has been added. Students are shown how to use MATLAB to plot functions, solve differential equations, and evaluate integrals. To make these techniques available to as large a group of students as possible, I also show how the free software package Octave can be used. The MATLAB programs in the first six chapters of this book run unchanged in either MATLAB or Octave.
As I shall show, however, the MATLAB programs in later chapters of the book must be modified slightly to run in Octave. Many of the electrical devices that have been developed within recent years are quantum devices. The finite potential well provides a fairly realistic description of the active region of a semiconductor laser. This book includes MATLAB programs that can be used to find the energy levels and wave functions for electrons confined to finite wells.
Another MATLAB program enables one to calculate the transmission and reflections coefficients for electrons incident upon a potential step where the potential energy changes discontinuously. Potential steps of this kind occur naturally at the interface between two different materials. By expressing the relation between the incoming and outgoing amplitudes of electrons incident xi www.com xii Preface upon an interface in matrix form, one can calculate the transmission and reflection coefficients for complex systems by multiplying the matrices for the individual parts. MATLAB and Octave programs described in Chapter 10 enable one to calculate transmission coefficients for barriers where the potential energy assumes a different value for a short interval and for more complex structures with two or three barriers.
Interesting interference effects occur for more than a single interface. This new edition also has new exercises using MATLAB and many more problems at the end of each chapter. In response to the request of several teachers of modern physics, all of the figures in the book will be placed at the website of the book and a digital copy of the book will be made available to teachers of modern physics upon request. Having the figures and a digital copy available makes it easier for teachers to prepare PowerPoint lectures.
THE NATURE OF THE BOOK As can be seen from the table of contents, Modern Physics for Scientists and Engineers covers atomic and solid-state physics before covering relativity theory. When I was beginning to teach modern physics, I led off with the special theory of relativity as do most books, but I found that this approach had a number of disadvantages. Following the short treatment of relativity, there was invariably an uncertain juncture when I made the transition back to a nonrelativistic framework in order to introduce the ideas of wave mechanics. The students were asked to make this transition when they were just getting started in the course.
Then, the important applications of relativity theory to particle and nuclear physics came at the end of the course when we had not used the relativistic formalism for some time. I found it to be better to develop nonrelativistic wave mechanics at the beginning of the course and “go relativistic” in the last 3 or 4 weeks. The course flows better that way. The first three chapters of this book give an introduction to quantum mechanics at an elementary level.
Chapters 4-6 are devoted to atomic physics and the development of lasers. Chapter 7 is devoted to statistical physics and Chapters 8-10 are devoted entirely to condensed matter physics. Each of these chapters has special features that cannot be found in any other book at this level. The new version of the Hartree-Fock applet described in Chapter 5 enables students to do Hartree-Fock calculations on any atom in the periodic table using the Hartree-Fock applet at the website of the book.
With the Hartree- Fock program of Charlottte Fischer in the background and a Java interface, the applet comes up showing the periodic table. A student can initiate a Hartree-Fock calculation by choosing a particular atom in the periodic table and clicking on the red arrow in the lower right-hand corner of the web page. The wave functions of the atom immediately appear on the screen and tabs along the upper edge of the web page enable students to gain additional information about the properties of the atom. One can find the average distance of each electron from the nucleus and evaluate the two-electron Slater integrals and the spin-orbit constant of the outer electrons.
When I cover the chapters on atomic physics in my course, I keep the focus on the underlying physics. As one moves from one atom to the next along a row of the periodic table, the nuclear charge increases. As a result, the electrons are drawn in toward the nucleus, and the distance between the electrons decreases. The Coulomb interaction between the electrons increases and the “LS” term structure expands.
All of this can be understood in simple physical terms. With the addition of MATLAB to Chapter 7, students can evaluate the probability that the values of the variables of particles lie within a particular range. This enables one to calculate the probability that the velocities of molecules in the upper atmosphere of a planet are greater than the escape velocity with the planet losing its atmosphere, and it enables one to calculate the fractional number of electrons in a semiconductor with an energy above the Fermi energy. In this new edition, Chapter 8 has a detailed description of graphene and carbon nanotubes.
One of my surprises in preparing the new edition was to find that the charge carriers of graphene are Fermions with zero mass that are accurately described by the Dirac equation. Physics is a whole with all of the individual pieces fitting together. Chapters 11 and 12, which are devoted to relativity theory, include a careful treatment of the Dirac equation and a qualitative description of quantum electrodynamics. Chapter 13 on particle physics includes a description of the conservation laws of lepton number, baryon number, and strangeness.
Also included is a treatment of the parity and charge conjugation symmetries, isospin, and the flavor and color SU(3) symmetries. The chapter on particle physics concludes with two new sections on local gauge invariance and the recent discovery of the Higgs boson. Most chapters of this book are fewer than 40 pages long, making it possible for an instructor to cover the main topics in each chapter in 1 week.