Undergraduate Lecture Notes in Physics Mark A. Cunningham Beyond Classical Physics Undergraduate Lecture Notes in Physics Undergraduate Lecture Notes in Physics (ULNP) publishes authoritative texts covering topics throughout pure and applied physics. Each title in the series is suitable as a basis for undergraduate instruction, typically containing practice problems, worked examples, chapter summaries, and suggestions for further reading. ULNP titles must provide at least one of the following: • An exceptionally clear and concise treatment of a standard undergrad- uate subject. • A solid undergraduate-level introduction to a graduate, advanced, or non-standard subject. • A novel perspective or an unusual approach to teaching a subject. ULNP especially encourages new, original, and idiosyncratic approaches to physics teaching at the undergraduate level. The purpose of ULNP is to provide intriguing, absorbing books that will continue to be the reader’s preferred reference throughout their academic career. Series editors Neil Ashby University of Colorado, Boulder, CO, USA William Brantley Furman University, Greenville, SC, USA Matthew Deady Bard College, Annandale-on-Hudson, NY, USA Michael Fowler University of Virginia, Charlottesville, VA, USA Morten Hjorth-Jensen University of Oslo, Oslo, Norway Michael Inglis SUNY Suffolk County Community College, Selden, NY, USA More information about this series at http://www.springer.com/series/ 8917 Mark A. Cunningham Beyond Classical Physics 123 Mark A. Cunningham Katy, TX, USA Wolfram Mathematica is a registered trademark of Wolfram Research, Inc ISSN 2192-4791 ISSN 2192-4805 (electronic) Undergraduate Lecture Notes in Physics ISBN 978-3-319-63159-2 ISBN 978-3-319-63160-8 (eBook) https://doi.org/10.1007/978-3-319-63160-8 Library of Congress Control Number: 2017946474 © Mark A. Cunningham 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland For Elizabeth Ann Preface Beyond Classical Physics is intended to be a sequel to the first-year level Neoclassical Physics. I have followed the same pathway, emphasizing the experimental underpinnings of our modern mathematical representations of nature. The focus here is primarily on the microscopic world, where experiments indicate that interactions of the constituents of matter are vastly different from those we observe in macroscopic objects. This world is best described by what we have come to call quantum theory. As we progress through the text, we shall endeavor to illustrate some of the historical contributions of the practitioners of the day. For example, Albert Einstein provoked a signal change in how physics is practiced with his development of a General Theory of Relativity but Einstein did not work completely in isolation. This text is not intended to be a history of the subject; indeed, we shall not attempt to provide attribution for every equation or experiment. Following such a path would lead to a publica- tion too ponderous to contemplate. Instead, my intent is to provide an introduction to the state of physics at the beginning of the twenty-first century. When I was a first-year graduate student, my electromagnetics instructor Feza Gürsey made a point of telling the class that Freeman Dyson had proved the renormalizability of quantum electrodynamics as a first-year student. Recently, Gerard t’Hooft had just proven the renormalizability of quantum chromodynamics at the one-loop level, also as a first-year stu- dent. “What,” he queried, “are you working on?” As he scanned the room, no one was willing to make eye contact, so I suppose that he concluded that ours was another class of misfits, without a single distinguished intellect amongst the lot. In retrospect and having sufficient time elapsed for Professor Gürsey’s stinging rebuke to have softened, I have come to another interpretation: Gürsey was seeking to challenge us to become relevant, to step beyond the limitations of curriculum and seek the frontiers of knowledge. Students have a natural tendency to follow the curriculum, learning whatever is set forth in textbooks and required in the syllabus. Universities have become complacent in their curriculum development, instead focussing on ad- ministrative, accreditation goals that reward adherence to (least common denominator) standards, not innovation. The result is that most students vii viii Preface do not see the frontiers of physics research until they are well into their graduate careers. It is a truly remarkable student who even knows what renormalization means at the first-year graduate level, much less have enough insight to contribute in a significant fashion. This is unfortunate, because renormalization became integrated into the physics literature by the 1950s. Physics has moved well beyond quantum electrodynamics. I have chosen to include the use not only of Mathematica software but also the numerical codes NWChem, that performs electronic structure calcu- lations, and NAMD/VMD that provide molecular dynamics and visual- ization/analysis capabilities. I recognize that these choices may seem to introduce an insurmountable obstacle to progress but tutorials in their use are available by their developers and the codes are freely accessible. In fact, given adequate computational resources, these codes can be used at the frontiers of research. These days, numerical simulation has risen to new importance. Experiment, of course, provides the defining result but often experiments need interpretation. Simulation, beyond ideal the- oretical formulations, provides concrete, if flawed, results that can help to explain experimental results and guide further experimentation. I have had undergraduate students utilize these codes to good effect. It takes discipline and hard work to become adept with these tools but stu- dents are generally quite enthralled with the results that they can obtain. They are brought to the precipice where they can begin to ask significant questions of their own. This is not a small achievement. While not a lengthy textbook, I expect that there is sufficient material to fill two semesters, particularly if instructors require students to attempt reading the original publications listed in each section. I have found this to be an interesting exercise for students. Even if they do not fully (or partly) comprehend the work, in many cases one finds that the original paper does not mention explicitly the reason why it is cited. Attribution follows reputation, in some instances. In any case, consulting the origi- nal literature is still an important step along the pathway to becoming a scientist. I believe it never too early to begin. That said, I recognize that in so short a work that there are many areas of physics that are not discussed. Again, my philosophy is that students will benefit more from investigating fewer topics in more detail than in pursuing a large quantity of topics, just to say that you’ve seen Bernoulli’s law, in case it comes up in a subsequent class. I believe that if students are properly prepared, they will have the tools to follow any topic that subsequently fires their imagination. As diligently as I have worked on this text, I admit that there are prob- ably mistakes; I hope there are no blatant falsehoods. Nevertheless, all Preface ix errors in the text are my responsibility and I apologize in advance for any particularly egregious examples. This work, of course, would never have been completed without the continual, and unflinching, support of my wife Liz. She has endured the creation of this book without complaint, even as I staggered through the effort. I cannot say thank you enough. Katy, TX, USA Mark A. Cunningham Contents Preface vii List of Figures xiii List of Tables xvii List of Exercises xix Chapter 1. Introduction 1 1.1. Perception as Reality 3 1.2. Classical Physics 11 1.3. Quantum Physics 17 1.4. Mathematical Insights 22 Chapter 2. On the Nature of the Photon 29 2.1. Maxwell’s Equations 30 2.2. Fields and Potentials 38 2.3. Point sources 44 2.4. Relativistic Formulation 48 2.5. Solitons 56 Chapter 3. On the Nature of the Electron 63 3.1. Dirac Equation 65 3.2.GaugeTheory 71 3.3. Gyromagnetic Ratio 77 3.4. Mathematical Difficulties 83 Chapter 4.OnAtoms 87 4.1.Hydrogen 88 4.2. Many-body Problems 96 4.3. Density-Functional Theory 102 4.4.HeavyAtoms 108 Chapter 5. On the Nature of the Nucleus 111 5.1. Electron Scattering 111 5.2. Nuclear Size 116 5.3. Nuclear Structure 120 5.4. Four Forces 129 Chapter 6. Toward a Theory of Everything 135 6.1. Quarks 136 xi xii Contents 6.2. Electroweak Unification 143 6.3. Standard Model 149 6.4.