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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.
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About the Authors
Jeremy Bernstein has had a dual career in physics and writing. He was on the staff of the New Yorker from 1963 to 1993 and was a Professor of Physics at the Stevens Institute of Technology from 1968 until his retirement in 1993, when he became Professor emeritus. He has won several awards for his writing about science and mountain travel. He has also published widely in both technical and non-technical journals. Some of his recent books are: An Introduction to Cosmology, Albert Einstein and the Frontiers of Physics, A Theory for Everything, In the Himalayas, and Dawning of the Raj. He has held visiting appointments at The Rockefeller University, The University of Islamabad, The Ecole Polytechnique, CERN laboratory, Princeton University, and Oxford. This photograph of Jeremy was taken on a bicycle trip in northern California. The thumb, which is on the grounds of the Clos Pegase art gallery and winery in Calistoga, was the work of the French artist Cesar Baldachini. Bernstein has bicycled in many countries including Bali and Crete. He makes his home in New York City and Aspen, Colorado.
Paul M. Fishbane
Paul Fishbane has been teaching undergraduate courses at the University of Virginia, where he is Professor of Physics, for some 25 years. He received his doctoral degree from Princeton University in 1967 and has published some 100 papers in his field, theoretical high energy physics. He is co-author of Physics for Scientists and Engineers with Stephen Gasiorowicz and Stephen Thornton. Paul has held visiting appointments at the State University of New York at Stony Brook, Los Alamos Scientific Laboratory, CERN laboratory in Switzerland, Amsterdam's NIKHEF laboratory, France's Institut de Physique Nucleaire, the University of Paris-Sud, and the Ecole Polytechnique. He has been active for many years at the Aspen Center for Physics, where current issues in physics are discussed with an international group of participants. His other interests include biking, music, and the physics of the kitchen. All of the rest of his time is spent trying to keep up with his family, especially his youngest son Nicholas.
Stephen Gasiorowicz was born in Poland and received his Ph.D. in physics at the University of California, Los Angeles in 1952. After spending 8 years at the Lawrence Radiation Laboratory in Berkeley, California, he joined the faculty of the University of Minnesota, where his field of research is theoretical high energy physics. As a visiting professor, he has traveled to the Niels Bohr Institute, NORDITA in Copenhagen, the Max Planck Institute for Physics and Astrophysics in Munich, DESY in Hamburg, Fermilab in Batavia, and the Universities of Marseille and Tokyo. He has been a frequent visitor and an officer of the Aspen Center for Physics. Steve is co-author of Physics for Scientists and Engineers with Paul Fishbane and Stephen Thornton and has written books on elementary particle physics and quantum physics. A relatively new occupation is that of grandfather, which still leaves some time for reading (history), biking, canoeing, and skiing.
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 semicon...
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