This classic, concise text has served a generation of physicists as an exceptionally useful guide to the mysteries of angular momenta and Clebsch-Gordon Coefficients. Derived from notes originally prepared to assist graduate students in reading research papers on atomic, molecular, and nuclear structure, the text first reviews the basic elements of quantum theory. It then examines the development of the fundamental commutation relations for angular momentum components and vector operators, and the ways in which matrix elements and eigenvalues of the angular momentum operators are worked out from the commutation relations.These chapters constitute a review on an elementary level of material usually included in a one-year course in quantum theory. In the second half of the text, the matrix elements of scalar, vector, and tensor operators are computed and applied to derive several useful relations in the theory of magnetic moments, electric quadruple moments, and dipole transition probabilities. Eschewing all that is irrelevant, this book focuses on the essentials and prepares readers for further study in the field. A helpful list of references concludes the work.

Notes on the Quantum Theory of Angular Momentum (Dover Books on Physics)

Science & Math

Physics

Feenberg, Eugene

Pake, George Edward

Mathematics

Dover Publications

This advanced undergraduate and graduate-level text introduces the power of operator theory as a tool in the study of quantum mechanics, assuming only a working knowledge of advanced calculus and no background in physics. The author presents a few simple postulates describing quantum theory, gradually introducing the mathematical techniques that help answer questions important to the physical theory; in this way, readers see clearly the purpose of the method and understand the accomplishment. The entire book is devoted to the study of a single particle moving along a straight line. By posing questions about the particle, the text gradually leads readers into the development of mathematical techniques that provide the answers. Lebesgue integration theory and complex variables are sometimes involved, but most of the book can be understood without them. Exercises at the end of each chapter provide helpful reinforcement.

Operator Methods in Quantum Mechanics (Dover Books on Physics)

Schechter, Martin

Geared toward readers already acquainted with special relativity, this book transcends the view of theory as a working tool to answer natural questions: What is a frame of reference? What is a "law of nature"? What is the role of the "observer"? Extensive, nonscientific treatment. 1983 edition.

A Sophisticate's Primer of Relativity: Second Edition (Dover Books on Physics)

Bridgman, P. W.

A completely self-contained, modern treatment of all the fundamental concepts essential to solving problems in electricity and magnetism, this volume also features numerous conceptual applications. A preliminary chapter offers background in coordinate systems, and six key chapters examine the operational definition of charge and current; the specification of arbitrary distributions of charge and current; the definition of the electromagnetic field and its effect on general charge distributions; the electric field produced by static charges; the magnetic induction field produced by steady currents; and Maxwell's equations in vacuum. These theoretical discussions are expanded in the subsequent chapters, which cover plane electromagnetic waves in vacuum; potential theory; conduction, dielectric polarization, and magnetization; Maxwell's equations in matter; plane electromagnetic waves in linear matter; radiation from prescribed sources in vacuum; and more

The Theory of the Electromagnetic Field (Dover Books on Physics)

Cook, David M.

A direct, stimulating approach to electromagnetic theory, this text employs matrices and matrix methods for the simple development of broad theorems. The author uses vector representation throughout the book, with numerous applications of Poisson’s equation and the Laplace equation (the latter occurring in both electronics and magnetic media). Contents include the electrostatics of point charges, distributions of charge, conductors and dielectrics, currents and circuits, and the Lorentz force and the magnetic field. Additional topics comprise the magnetic field of steady currents, induced electric fields, magnetic media, the Maxwell equations, radiation, and time-varying current circuits. Geared toward advanced undergraduate and first-year graduate students, this text features a large selection of problems. It also contains useful appendixes on vector analysis, matrices, elliptic functions, partial differential equations, Fourier series, and conformal transformations. 228 illustrations by the author. Appendixes. Problems. Index.

Introduction to Electromagnetic Theory (Dover Books on Physics)

Owen, George E.

Written by a well-known professor of physiology at McGill University, this text presents an informative exploration of the basis of the Second Law of Thermodynamics, detailing the fundamental dynamic properties behind the construction of statistical mechanics.Topics include maximal entropy principles; invertible and noninvertible systems; ergodicity and unique equilibria; asymptotic periodicity and entropy evolution; and open discrete and continuous time systems. The author demonstrates that the black body radiation law can be deduced from maximal entropy principles; discusses sufficient conditions for the existence of at least one state of thermodynamic equilibrium; describes the behavior of entropy in asymptotically periodic systems and the necessary and sufficient condition for the evolution of entropy to a global maximum; and presents the three main types of ergodic theorems and theory proofs. He also explores the potential of incomplete knowledge of dynamical variables, measurement imprecision, and the effects of noise in entropy increases.Geared toward physicists and applied mathematicians with an interest in the foundations of statistical mechanics, this text is suitable for advanced undergraduate and graduate courses.

Time's Arrow: The Origins of Thermodynamic Behavior (Dover Books on Physics)

Mackey, Michael C.

Concise and practical, this text by a renowned teacher sketches the mathematical background essential to understanding the fundamentals of relativity theory. Subjects include the velocity of light, measurement of time and distance, and properties of mass and momentum, with numerous diagrams, formulas, and examples, plus exercises and solutions. 1960 edition.

Readable Relativity (Dover Books on Physics)

Durell, Clement V.

An intermediate course in optics, this volume explores both experimental and theoretical concepts, offering practical knowledge of geometrical optics that will enhance students' comprehension of any relevant applied science. Its exposition of the concepts of classical optics is presented with a minimum of mathematical detail but presumes some knowledge of calculus, vectors, and complex numbers. Subjects include light as wave motion; superposition of wave motions; electromagnetic waves; interaction of light and matter; velocities and scattering of light; polarized light and dielectric boundaries; double refraction; and the interference of two sources laterally separated. Additional topics cover Fresnel and Fraunhofer diffraction; coherent sources separated in depth; applications of physical optics; images of points by single surfaces and by systems of surfaces; magnification, aperture, and field; and image defects. Illustrative problems appear throughout the text, assuring students of an opportunity to attain a full understanding of the material. The appendixes feature short topics of lively research interest that can be used simply for reference or formally incorporated by the instructor into the course.

Concepts of Classical Optics (Dover Books on Physics)

Strong, John

Many books explore group theory’s connection with physics, but few of them offer an introductory approach. This text provides upper-level undergraduate and graduate students with a foundation in problem solving by means of eigenfunction transformation properties. This study focuses on eigenvalue problems in which differential equations or boundaries are unaffected by certain rotations or translations. Its explanation of transformations induced in function space by rotations (or translations) in configuration space has numerous practical applications — not only to quantum mechanics but also to any other eigenvalue problems, including those of vibrating systems (molecules or lattices) or waveguides. Points of special interest include the development of Schur's lemma, which features a proof illustrated with a symbolic diagram. The text places particular emphasis on the geometric representation of ideas: for instance, the similarity transformation is characterized as a rotation in multidimensional function space and the reduction is described in terms of mutual orthogonal spaces. General references provide suggestions for further study, citing works of particular clarity and readability.

Group Theory: The Application to Quantum Mechanics (Dover Books on Physics)

Meijer, Paul H. E.

Bauer, Edmond

This volume demonstrates the manner in which statistical mechanics can be built up deductively from a small number of well-defined physical assumptions. A solid basis for the deductive structure is provided by embodying these assumptions in a system of five postulates that describe an idealized model of real physical systems. These postulates play a theoretical role similar to that of the first and second laws in thermodynamics. The first chapter concerns the primary physical assumptions and their idealization in the form of postulates. The following three chapters examine the consequences of these postulates, culminating in the derivation of the fundamental formulas for calculating probabilities in terms of dynamical quantities. Two concluding chapters are devoted to an analysis of the notion of entropy, illustrating its links between statistical mechanics and thermodynamics and between statistical mechanics and communication theory. Because this book deals mostly with general principles, its only detailed considerations of physical applications are in terms of the system with the simplest possible dynamics: the ideal classical gas, which is discussed both in its equilibrium and its nonequilibrium aspects. Intended for readers with a knowledge of physics at the advanced undergraduate and graduate levels, this volume considers topics of interest not only to physicists, but also to statisticians, communication theorists, chemists, and mathematicians.

Foundations of Statistical Mechanics: A Deductive Treatment (Dover Books on Physics)

Penrose, Oliver

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