Modern Physics

Preface

Knowledge of the revolutions of 20th-century physics is an indispensable part of the training of any engineer and physical scientist. That is because virtually all of today's technology is based, at least in part, on this knowledge. The basic subject material of what is called modern physics is very nearly 100 years old, so that it is hardly modern at all. Yet just as Newton's laws, today 300 years old, Maxwell's equations, today nearly 150 years old, and the laws of classical statistical physics, more than 100 years old, remain applicable and essential in their respective domains of physical law, so too do the two major developments of the first half of this century: relativity and quantum mechanics. These fundamental subjects underlie a vast scope of application that continues its inventive course today. Moreover, research on fundamental physics has not stopped with relativity and quantum mechanics, and working scientists still face questions as interesting as any that have been answered in the past.

Both relativity and quantum mechanics require the student to make difficult changes in how he or she thinks the physical world works. The subjects violate prejudices that have been built up by everyday experience. For this reason, precision and clarity of explanation are, for us, the first and most important part of the material. We have made every effort to avoid the "it can be shown" approach and to present modern physics in a way that makes its interconnectedness, as well as its connection to classical physics, evident.

Throughout this text, we have built in a historical approach - a discussion of how a subject developed and the thinking that led to its maturation. Often this historical perspective is interwoven with the material; at other times it would interrupt an efficient and compact presentation, and then we present it on the side, as it were. We feel that this approach is useful in that it stresses that the roots of the revolutionary advances lie in experiment; it also makes the text more fun to read.

The book forms the basis of a traditional course in the subject. It contains, in a mathematical language that we have deliberately kept at a level we felt students would be comfortable with, descriptions of special relativity and of the laws of quantum mechanics. It describes applications of these fundamental ideas to both technological and scientific issues. Finally, it describes the subject matter that is of fundamental interest today. All this material is too much to cover in one semester, the usual length of time for such courses, so a more detailed explanation of what we do is in order. This will allow the instructor to make a reasonable choice of what to cover and provide guidance to the reader or the use of the material in the book.

We have broken the material into several parts, even if the boundary between the coverage of the different parts is not always perfectly sharp. The first chapter replaces what would otherwise be a steady set of footnotes referring the reader to an introductory calculus-based textbook. In other words, Chapter 1 is a place to remind students of things that, ideally, they should have fully absorbed in their introductory courses. While the chapter cannot replace such a textbook, it can be a convenient road map to the introductory material. It also constitutes a type of formulary of classical physics. But we urge the student to keep his or her introductory text and to consult it when necessary. The chapter contains no examples or problems, and it is not meant to be assigned as normal course material.

Part 1 consists of two chapters on special relativity. These are divided more or less according to traditional lines, with a discussion of space and time in one chapter and momentum and energy in the next. Our approach is to extract length contraction from the Michelson-Morley result and use it as a jumping off point for the other effects of special relativity, including the Lorentz transformations. This tack differs somewhat in detail, although not in spirit, from the approach that abstracts special relativity from a moving light-clock. We believe that the formal approach starting early with the full set of Lorentz transformations, less suitable for physicists and engineers than mathematicians, can miss the physics of the subject. We also save our discussion of general relativity for a much later chapter. Even though the origins of general relativity are old, there is much exciting current material to cover.

Part 2 is a treatment of the fundamental laws of quantum mechanics. This is a subject with a fascinating yet complex history, but we feel that the number of missteps in the development of quantum mechanics speak against a full historical interweaving of the material with the rest of the text. Thus a separate historical introduction is presented. Chapter 4 describes the experimental data that could not be encompassed by classical physics and examines the daring ideas that opened the gateway to the development of quantum mechanics. Bohr's approach to the structure of the hydrogen atom provided the critical breakthrough, and it merits a chapter on its own, Chapter 5. Extended to circular orbits for other central forces, that approach leads to the quantum nature of rotational and vibrational motion, and it also provides a useful tool for the dependence of energy levels on the relevant physical parameters.

Chapter 6 introduces the Schrodinger equation. Here the problem is to find a way to present this material without getting too heavily into mathematics. One common approach is via wave packets, but they are something with which many students using this text may feel uncomfortable. Instead, we motivate the Schrodinger equation by using classical parallels and the physical meaning of a wave function to argue the form of the Schrodinger equation. This involves bringing in the probability interpretation of the wave function in what we feel is its proper place: right at the beginning. We have kept the mathematics involved in actually solving the Schrodinger equation low, treating just the infinite well here. Only in Chapter 7 do we go into the addition of plane waves with easily managed distributions to get at the concepts of wave packets and of probabilities for measurements of momentum. In that way we can understand the particlelike behavior of a superposition of waves. This material also allows us to introduce the uncertainty relations. We show how they "shield" quantum mechanics from contradictions, and we illustrate their utility in making estimates of ground-state energies.

Starting with Chapter 8 we are in position to see what the Schrodinger equation has to say about some interesting potentials, namely barriers and wells. A good deal of useful physics about scattering and bound states can be conveyed for these mathematically simple situations. We pay particular attention to the physics of tunneling, relating it to internal reflection and to a demonstration that can actually be done in class and describing where it is relevant to physical phenomena. Chapter 9 is a discussion of the Schrodinger equation in the context of the coulomb potential. It is in this chapter that we treat angular momenta, even if we do not employ much in the way of mathematical rigor, and our discussion of the hydrogen atom is concentrated in this chapter, along with the Zeeman effect and the concept of spin. In Chapter 10 we conclude our discussion of the principles of quantum mechanics with the treatment of manybody systems and the symmetry of the wave function for identical particles. This subject is indispensable for an understanding of solids and other material systems, and by putting the exclusion principle here we are prepared for its applications in many domains.

Part 3 of the book is labeled "applications," and it contains discussions of those areas, both in nature and in technology, that cannot be understood without quantum mechanics. The instructor can easily pick and choose among the chapters in this part of the text if he or she is pressed for time. Still, one needs to be aware that there are constraints in some cases; for example, it would be difficult to teach the physics of semiconductors without having first seen the Fermi-Dirac distribution.

Part 3 begins (in Chapter 11) with a discussion of complex atoms and of molecules. We are primarily interested in the quantum mechanical basis of the periodic table, in the way that minima in energy are associated with the mechanisms by which atoms can form molecules, and in simple molecular spectra. The next chapter is a treatment of thermal systems, and because some of the students who take this course may not have had a good background in that material we begin with a simple treatment of classical statistical mechanics, an extremely useful subject for any future engineer or scientist. A treatment of specific heats allows us to understand why one needs a discussion of statistical quantum mechanics. The Boltzmann distribution, a major target, is not only extremely important on its own, it also provides a guide for the development of the quantum mechanical distributions for identical particles. In each case, very simple arguments based on the idea of thermal equilibrium are used. We can also make the connection back to the blackbody distribution first described in Chapter 4, closing a circle.

In Chapter 13 we describe how one can think about unstable systems in quantum mechanics, a topic relevant to atoms in excited states and, by extension, to lasers, whose operation and use form a major part of the chapter. Chapter 14 describes applications to the solid state, a topic so large that we have been forced to make some restrictive choices. We have tried in part to choose according to topics of the greatest current interest to engineers. Accordingly, we have begun with a treatment of how electricity is conducted in materials. When this is coupled with the essential description of band structure, we are led in a natural way to the behavior of semiconductors, a subject with exceptionally rich, diverse applications. We nevertheless restrict ourselves to the more comprehensible topics, leaving out a detailed treatment of many of the more complicated one s- the many varieties of transistors, for example. We also take the opportunity to describe what we think are the most interesting and physically significant aspects of superconductivity The last chapter in this part, Chapter 15, contains a selection of topics in nuclear physics. The subject is a complex one, and we have chosen on the basis of what we think will illuminate best its various facets; the applications that we examine are equally diverse.

Part 4 of the text contains a discussion of topics that are, at least in part, at the forefront of the unknown. We think it important that students - even students who are going to work in highly applied areas - be exposed to this sort of material. It helps to dispel the notion that the subject is a closed one in which all one has to do is know how to plug things into formulas, and it emphasizes the overarching role that simple scientific curiosity plays. The three chapters of this part treat, respectively, elementary particle physics, general relativity, and cosmology. While general relativity per se is old, it is deeply implicated in our understanding of cosmological issues, and its reconciliation with quantum mechanics represents one of the great unanswered questions. Particle physics, too, is an important piece of the puzzle that cosmologists are attempting to assemble.

Chapter 16, on particle physics, addresses the unanswered questions of just what are the underlying laws that govern all the other aspects of matter we have described in this book. It is a highly qualitative and descriptive chapter, but it is also a modern one, concentrating on those issues that are actively addressed today. In addition to covering the older topics, the chapter on general relativity contains a deeper and more physical discussion of such issues as black holes and gravitational radiation than is usual. We think these issues are of great interest to students. The chapter on cosmology speaks to the question of the nature of the universe; this chapter also contains a detailed discussion of the motivation and evidence for the big bang. The discussion of the evolution of the universe from a big bang brings in many of the topics we have discussed throughout and, we hope, will convey the fundamental unity of physics to the reader.

We would like to offer thanks for the considerable help we were given in the process of writing this book. In addition to the many scientific colleagues who clarified issues we did not understand well enough, we want to thank our editor Alison Reeves, our developmental editor David Chelton, and our production editor Joanne Hakim. Many others at Prentice Hall have helped us, too. In particular, we want to thank Yvonne Gerin and Ray Mullaney. We would also like to acknowledge the following reviewers, who provided valuable feedback.

Albert Altman
University of Massachusetts, Lowell

David Curott
University of North Alabama

Luther Frommhold
University of Texas, Austin

Richard T. Hammond
Rensselaer Polytechnic Institute

Roger J. Hanson
University of Northern Iowa

Edward Hart
University of Tennessee, Knoxville

Gary G. Ihas
University of Florida

Rondo Jeffery
Weber State University

John Kenny
Bradley University

Sanford Kern
Colorado State University

John M. Knox
Idaho State University

Arthur Z. Kovacs
Rochester Institute of Technology

Curt Larson
University of Wisconsin, River Falls

Paul L. Lee
California State University, Northbridge

Nathaniel P Longley
Colorado College

Wolfgang Lorenzon
University of Michigan

Thomas Moses
Knox College

Joseph F. Owens III
Florida State University, Tallahassee

Stephen Pate
New Mexico State University

Joseph Priest
Miami University

Robert Ross
University of Detroit, Mercy

Weidian C. Shen
Eastern Michigan University

Paul Sokol
Pennsylvania State University

Takamasa Takahashi
St. Norbert College

Frank C. Taylor
Furman University (now retired)

Larry H. Toburen
East Carolina University

Jack Tuszynski
University of Alberta

C. Wesley Walter
Dension University

Jeffrey L. Wragg
College of Charleston

This comprehensive book provides the most complete coverage of general relativity and cosmology—with detailed discussions on the historical origins of topics. Its presentation is consistently linked to observation, and to the physical numbers as well, so that readers develop a sense of the magnitudes involved in the material being covered. Chapter topics include waves as particles and particles as waves; atoms and the Bohr Model; The Schrödinger Equation; barriers and wells; statistical physics; conductors, insulators, and superconductors; and elementary particle physics. A reference for today's scientists.

1. A Review.

I. RELATIVITY.

2. The Basics of Relativity.
3. Consequences of Relativity.

II. THE ORIGINS OF QUANTUM MECHANICS.

4. Waves as Particles and Particles as Waves.
5. Atoms and the Bohr Model.
6. The Schrödinger Equation.
7. Classical and Unclassical behavior: Wave Packets and Uncertainty.
8. Barriers and Wells.
9. The Hydrogen Atom.
10. Many Particles.

III. APPLICATIONS.

11. Complex Atoms and Molecules.
12. Statistical Physics.
13. Atoms, Radiation and Lasers.
14. Conductors, Insulators, and Superconductors.
15. The Atomic Nucleus.

IV. FRONTIERS.

16. Elementary Particle Physics.
17. General Relativity.
18. Cosmology.

Appendix A: Physical Constants
Appendix B: Mathematics.