Dover Books on Physics
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The Kinematics of Vorticity
by Clifford Truesdell
Part of the Dover Books on Physics series
This unique graduate-level monograph offers a heavily mathematical treatment of the vorticity of fluids. The subject's wealth of applications extends to many areas of physics and engineering, and the book will also appeal to mathematically oriented historians of science. Starting with consideration of geometrical and kinematical preliminaries, the text advances to examinations of vorticity, the vorticity field, vorticity measures, and vorticity averages. Subsequent chapters explore Bernoullian theorems, convection and diffusion of vorticity, and circulation-preserving motions.
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Beta Decay for Pedestrians
by Harry J. Lipkin
Part of the Dover Books on Physics series
The "pedestrian approach" was developed to describe some essentially simple experimental results and their theoretical implications in plain language. In this graduate-level text, Harry J. Lipkin presents simply, but without oversimplification, the aspects of beta decay that can be understood without reference to the formal theory; that is, the reactions that follow directly from conservation laws and elementary quantum mechanics. The pedestrian treatment is neither a substitute for a complete treatment nor a watered-down version. Its derivation of results obtainable without the formal theory makes these results more understandable and less mysterious to those who have neither the time nor the inclination to master the details of the theory. On the other hand, those already acquainted with the formal theory will find in the pedestrian treatment a clear distinction between results dependent on the specific assumptions underlying the formal theory and those independent of these assumptions, which follow from simple general principles. Since peculiar experimental results are an ever-present possibility, it is always useful to have a simple method of evaluating challenges to theoretical assumptions or approximations.
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Green's Functions and Condensed Matter
by G. Rickayzen
Part of the Dover Books on Physics series
Green's functions, named for the mathematician who developed them in the 1830s, possess applications in many areas of physics. This volume presents the basic theoretical formulation, followed by specific applications, and is suitable for advanced undergraduates, graduate students, and professionals in the area of condensed matter physics. Beginning with a description of Green's function in classical physics from a modern point of view, the text progresses to the definition and properties of Green's functions in quantum physics. Most of the book explores applications, focusing on transport coefficients of a metal, the Coulomb gas, Fermi liquids, electrons and phonons, superconductivity, superfluidity, and magnetism. The treatment assumes a good working knowledge of quantum mechanics and a familiarity with the occupation number representation. An appendix provides the main formulas and the correspondence with wave mechanics. Each chapter concludes with references and problems for further study.
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Fundamental Formulas of Physics, Volume Two
by Donald H. Menzel
Part of the Dover Books on Physics series
The republication of this book, unabridged and corrected, fills the need for a comprehensive work on fundamental formulas of mathematical physics. It ranges from simple operations to highly sophisticated ones, all presented most lucidly with terms carefully defined and formulas given completely. In addition to basic physics, pertinent areas of chemistry, astronomy, meteorology, biology, and electronics are also included. This is no mere listing of formulas, however. Mathematics is integrated into text, for the most part, so that each chapter stands as a brief summary or even short textbook of the field represented. The book, therefore, fills other needs than the primary function of reference and guide for research. The student will find it a handy review of familiar fields and an aid to gaining rapid insight into the techniques of new ones. The teacher will study it as a useful guide to a broad concept of physics. The chemist, astronomer, meteorologist, biologist, and engineer will not only derive valuable aid from their special chapters, but will understand how their specialty fits into the large scheme of physics. Vol. 1 chapter titles: Basic Mathematical Formulas, Statistics, Nomograms, Physical Constants, Classical Mechanics, Special Theory of Relativity, The General Theory of Relativity, Hydrodynamics and Aerodynamics, Boundary Value Problems in Mathematical Physics, Heat and Thermodynamics, Statistical Mechanics, Kinetic Theory of Gases: Viscosity, Thermal Conduction, and Diffusion, Electromagnetic Theory, Electronics, Sound and Acoustics. Vol. 2 chapter titles: Geometrical Optics, Physical Optics, Electron Optics, Molecular Spectra, Atomic Spectra, Quantum Mechanics, Nuclear Theory, Cosmic Rays and High-Energy Phenomena, Particle Accelerators, Solid State, Theory of Magnetism, Physical Chemistry, Basic Formulas of Astrophysics, Celestial Mechanics, Meteorology, Biophysics.
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Lie Groups for Pedestrians
by Harry J. Lipkin
Part of the Dover Books on Physics series
According to the author of this concise, high-level study, physicists often shy away from group theory, perhaps because they are unsure which parts of the subject belong to the physicist and which belong to the mathematician. However, it is possible for physicists to understand and use many techniques which have a group theoretical basis without necessarily understanding all of group theory. This book is designed to familiarize physicists with those techniques. Specifically, the author aims to show how the well-known methods of angular momentum algebra can be extended to treat other Lie groups, with examples illustrating the application of the method. Chapters cover such topics as a simple example of isospin; the group SU3 and its application to elementary particles; the three-dimensional harmonic oscillator; algebras of operators which change the number of particles; permutations; bookkeeping and Young diagrams; and the groups SU4, SU6, and SU12, an introduction to groups of higher rank. Four appendices provide additional valuable data.
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Treatise on Irreversible and Statistical Thermodynamics
An Introduction to Nonclassical Thermodynamics
by Wolfgang Yourgrau
Part of the Dover Books on Physics series
Extensively revised edition of a much-respected work examines thermodynamics of irreversible processes, general principles of statistical thermodynamics, assemblies of noninteracting structureless particles, and statistical theory. 1966 edition.
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Theoretical Hydrodynamics
by L. M. Milne-Thomson
Part of the Dover Books on Physics series
This classic exposition of the mathematical theory of fluid motion is applicable to both hydrodynamics and aerodynamics. Based on vector methods and notation with their natural consequence in two dimensions - the complex variable - it offers more than 600 exercises and nearly 400 diagrams. Prerequisites include a knowledge of elementary calculus. 1968 edition.
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Noise and Fluctuations
An Introduction
by D. K. C. MacDonald
Part of the Dover Books on Physics series
An understanding of fluctuations and their role is both useful and fundamental to the study of physics. This concise study of random processes offers graduate students and research physicists a survey that encompasses both the relationship of Brownian Movement with statistical mechanics and the problem of irreversible processes. It outlines the basics of the physics involved, without the strictures of mathematical rigor. The three-part treatment starts with a general survey of Brownian Movement, including electrical Brownian Movement and "shot-noise," Part two explores correlation, frequency spectrum, and distribution function, with particular focus on application to Brownian Movement. The final section examines noise in electric currents, including noise in vacuum tubes and a random rectangular current. Frequent footnotes amplify the text, along with an extensive selection of Appendixes.
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Applied Optics and Optical Design, Part One
by A. E. Conrady
Part of the Dover Books on Physics series
Part I covers all ordinary ray-tracing methods, together with the complete theory of primary aberrations and as much of higher aberration as is needed for the design of telescopes, low-power microscopes and simple optical systems. Chapters: Fundamental Equations, Spherical Aberration, Physical Aspect of Optical Images, Chromatic Aberration, Design of Achromatic Object-Glasses, The Optical Sine Theorem, Trigonometric Tracing of Oblique Pencils, General Theory of Perfect Optical Systems, and Ordinary Eyepieces. Part II extends the coverage to the systematic study and design of practically all types of optical systems, with special attention to high-power microscope objectives and anastigmatic photographic objectives. Edited and completed from the author s manuscript by Rudolf Kingslake, Director of Optical Design, Eastman Kodak Company. Chapters: Additional Solutions by the Thin-Lens Method , Optical Path Differences, Optical Path Differences at an Axiallmage Point, Optical Tolerances, Chromatic Aberration as an Optical Path Difference, The Matching Principle and the Design of Microscope Objectives, Primary Aberrations of Oblique Pencils, Analytical Solutions for Simple Systems with Remote Stop, Symmetrical Photographic Objectives, and Unsymmetrical Photographic Objectives.
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Statistical Physics
A Probabilistic Approach
by Bernard H. Lavenda
Part of the Dover Books on Physics series
Suitable for graduate students in chemical physics, statistical physics, and physical chemistry, this text develops an innovative, probabilistic approach to statistical mechanics. The treatment employs Gauss's principle and incorporates Bose-Einstein and Fermi-Dirac statistics to provide a powerful tool for the statistical analysis of physical phenomena. The treatment begins with an introductory chapter on entropy and probability that covers Boltzmann's principle and thermodynamic probability, among other topics. Succeeding chapters offer a case history of black radiation, examine quantum and classical statistics, and discuss methods of processing information and the origins of the canonical distribution. The text concludes with explorations of statistical equivalence, radiative and material phase transitions, and the kinetic foundations of Gauss's error law. Bibliographic notes complete each chapter.
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Neutrons, Nuclei and Matter
An Exploration Of The Physics Of Slow Neutrons
by James Byrne
Part of the Dover Books on Physics series
Hailed as "an excellent survey" by Physics Today, this encyclopedic reference covers virtually every aspect of neutron physics. Its accessible treatment constitutes a major compilation of fundamental properties and interactions. 1994 edition.
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Stellar Evolution, Nuclear Astrophysics, and Nucleogenesis
by A. G. W. Cameron
Part of the Dover Books on Physics series
A landmark in the development of nuclear astrophysics, this work addresses interrelated questions - What are stars? How does the sun shine? - that have puzzled observers from time immemorial. 1957 edition.
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The Theory of Linear Viscoelasticity
by D. R. Bland
Part of the Dover Books on Physics series
This concise introduction to the concepts of viscoelasticity focuses on stress analysis. Three detailed individual sections present examples of stress-related problems. In addition, it explains procedures for model fitting to measured values of complex modulus or compliance. The text begins with an introduction to the concepts of viscoelasticity. Succeeding chapters explore the foundations of three-dimensional linear viscoelasticity and stress analysis. Sinusoidal oscillation problems, quasi-static problems, and dynamic problems receive particular attention. The final chapter examines model fitting to measured values of complex modulus or compliance. Numerous examples and figures illuminate the text.
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Foundations of Radiation Hydrodynamics
by Dimitri Mihalas
Part of the Dover Books on Physics series
Excellent, informative volume focuses on dynamics of nonradiating fluids, problems involving waves, shocks and stellar winds, physics of radiation, radiation transport, and the dynamics of radiating fluids. 1984 edition.
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Thermoelectricity
An Introduction to the Principles
by D. K. C. MacDonald
Part of the Dover Books on Physics series
This introductory treatment provides an understanding of the fundamental concepts and principles involved in the study of thermoelectricity in solids and of conduction in general. Aimed at graduate-level students and those interested in basic theory, it will be especially valuable to experimental physicists working in fields connected with electron transport and to theoreticians seeking a survey of thermoelectricity and related questions. Chronicling the early history of thermoelectricity from its discovery to modern times, this text features a considerable amount of experimental data and discusses these findings at length wherever they bear a particular relevance to theory. The author, a well-known authority in this field, draws heavily from his own work on thermoelectrical phenomena as they are observed in the study of metals. Numerous illustrative figures appear throughout the text.
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Applied Optics and Optical Design, Part Two
by A. E. Conrady
Part of the Dover Books on Physics series
This two-volume paperback republication of A. E. Conrady's classic work presents his complete system of optical design. The only work of its kind in English, this set leads the reader step by step from the fundamental concepts of geometrical and physical optics up to the point where he can design the simpler optical systems without aid. It remains the only detailed work on the subject written with the needs of the practical designer and the self-taught constantly in mind. For most of the text, no mathematics above trigonometry is needed; occasional sections require some calculus and analytical geometry. Part I covers all ordinary ray-tracing methods, together with the complete theory of primary aberrations and as much of higher aberration as is needed for the design of telescopes, low-power microscopes and simple optical systems. Chapters: Fundamental Equations, Spherical Aberration, Physical Aspect of Optical Images, Chromatic Aberration, Design of Achromatic Object-Glasses, Extra-Axial Image Points, The Optical Sine Theorem, Trigonometric Tracing of Oblique Pencils, General Theory of Perfect Optical Systems, and Ordinary Eyepieces. Part II extends the coverage to the systematic study and design of practically all types of optical systems, with special attention to high-power microscope objectives and anastigmatic photographic objectives. Edited and completed from the author's manuscript by Rudolf Kingslake, Director of Optical Design, Eastman Kodak Company. Chapters: Additional Solutions by the Thin-Lens Method, Optical Path Differences, Optical Path Differences at an Axial Image Point, Optical Tolerances, Chromatic Aberration as an Optical Path Difference, The Matching Principle and the Design of Microscope Objectives, Primary Aberrations of Oblique Pencils, Analytical Solutions for Simple Systems with Remote Stop, Symmetrical Photographic Objectives, and Unsymmetrical Photographic Objectives.
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Theories of Figures of Celestial Bodies
by Wenceslas S. Jardetzky
Part of the Dover Books on Physics series
Suitable for upper-level undergraduates and graduate students, this text explores the most exact methods used in the theory of figures of equilibrium. It also examines problems concerning the figures of celestial bodies, including invariable or varying figures, zonal rotation, systems composed of fluid and rigid parts, and more. 1958 edition.
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Finite Quantum Electrodynamics
The Causal Approach
by Gunter Scharf
Part of the Dover Books on Physics series
The third edition of this classic graduate-level physics text contains the author's revisions and corrections plus a brief new Epilogue. Subjects include relativistic quantum mechanics, field quantization, causal perturbation theory, properties of the S-matrix, and considerations of other electromagnetic couplings. Includes problems for each chapter and four appendices. 2013 edition.
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Laser Light Scattering
Basic Principles and Practice
by Benjamin Chu
Part of the Dover Books on Physics series
Geared toward upper-level undergraduate and graduate students, this text introduces the interdisciplinary area of laser light scattering. It focuses chiefly on quasielastic laser scattering, discussing theoretical concepts at a realistic level. Some background in the physical sciences is assumed, but the opening chapters offer a brief review of classical electricity and magnetism as well as the general scattering theory. Topics include basic theoretical concepts related to light mixing spectroscopy, characteristics of the Fabry-Perot interferometer, and photon-counting fluctuations. The author, a distinguished professor in the Department of Chemistry at Stony Brook University, discusses experimental methods, including setting up a light scattering spectrometer using digital photon-counting and correlation techniques. Subsequent chapters explore applications to macromolecular systems, anemometry and its utility in reaction kinetics, and critical opalescence. References appear throughout the text.
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States of Matter
by David L. Goodstein
Part of the Dover Books on Physics series
Overview covers thermodynamics and statistical mechanics; gases, solids, and liquids; perfect gases; electronics in metals; and the Bose condensation. Also: structure of a fluid, potential energy, interacting gases and liquids, Weiss molecular field theory, van der Waals equation, and other pertinent aspects of phase transitions. 154 figures .1975 edition.
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X-Ray Diffraction
In Crystals, Imperfect Crystals, and Amorphous Bodies
by A. Guinier
Part of the Dover Books on Physics series
Superb study begins with fundamentals of x-ray diffraction theory using Fourier transforms, then applies general results to various atomic structures, amorphous bodies, crystals and imperfect crystals. Elementary laws of x-ray diffraction on crystals follow as special case. Highly useful for solid-state physicists, metallographers, chemists, and biologists. 154 illustrations. 1963 edition.
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Quantum Mechanics in Hilbert Space
by Eduard Prugovecki
Part of the Dover Books on Physics series
A critical presentation of the basic mathematics of nonrelativistic quantum mechanics, this text is suitable for courses in functional analysis at the advanced undergraduate and graduate levels. Its readable and self-contained form is accessible even to students without an extensive mathematical background. Applications of basic theorems to quantum mechanics make it of particular interest to mathematicians working in functional analysis and related areas. This text features the rigorous proofs of all the main functional-analytic statements encountered in books on quantum mechanics. It fills the gap between strictly physics- and mathematics-oriented texts on Hilbert space theory as applied to nonrelativistic quantum mechanics. Organized in the form of definitions, theorems, and proofs of theorems, it allows readers to immediately grasp the basic concepts and results. Exercises appear throughout the text, with hints and solutions at the end.
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Ferrohydrodynamics
by R. E. Rosensweig
Part of the Dover Books on Physics series
The behavior and dynamics of magnetic fluids receive a coherent, comprehensive treatment in this high-level study. One of the best classical introductions to the subject, the text covers most aspects of particle interaction, from magnetic repulsion to quasi-stable equilibriums and ferrohydrodynamic instabilities. Suitable for graduate students and researchers in physics, engineering, and applied mathematics.
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The Principle of Relativity with Applications to Physical Science
by Alfred North Whitehead
Part of the Dover Books on Physics series
An exposition of an alternative rendering of the theory of relativity, this volume is the work of the distinguished English mathematician and philosopher, Alfred North Whitehead. Suitable for upper-level undergraduates and graduate students, its three-part treatment begins with an overview of general principles that may be described as mainly philosophical in character. Part II is devoted to physical applications and chiefly concerns the particular results deducible from the formulas assumed for the gravitation and electromagnetic fields. The final part consists of an exposition of the elementary theory of tensors.The author notes that the text's order proceeds naturally from general principles to particular applications, concluding with a general exposition of the mathematical theory, special examples of which have occurred in the discussion of the applications. Physicists,Whitehead suggests, may prefer to start with Part II, referring back to a few formulas mentioned at the end of Part I, and mathematicians may start with Part III. The whole evidence, he adds, requires a consideration of all three parts.
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Gravitational Curvature
An Introduction To Einstein's Theory
by Theodore Frankel
Part of the Dover Books on Physics series
This classic text and reference monograph applies modern differential geometry to general relativity. A brief mathematical introduction to gravitational curvature, it emphasizes the subject's geometric essence and stresses the global aspects of cosmology. 1979 edition.
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Reflections on the Motive Power of Fire
And Other Papers On The Second Law Of Thermodynamics
by Sadi Carnot
Part of the Dover Books on Physics series
The title essay, along with related papers in this volume, laid the foundation of modern thermodynamics. Highly readable, it contains no arguments that depend on calculus. Translation of 1890 edition.
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Lightning
by Martin A. Uman
Part of the Dover Books on Physics series
Revised, updated edition of classic work on the physics of lightning covers phenomena, terminology, measurement, photography, spectroscopy, thunder, and more, including reviews of recent research. 140 figures and tables.
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Einstein's Theory of Relativity
by Max Born
Part of the Dover Books on Physics series
Semi-technical account includes a review of classical physics (origin of space and time measurements, Ptolemaic and Copernican astronomy, laws of motion, inertia, more) and of Einstein's theories of relativity.
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Treatise on Thermodynamics
by Max Planck
Part of the Dover Books on Physics series
Written by the founder of quantum theory, a Nobel Prize winner, this classic volume is still recognized as among the best introductions to thermodynamics. It is a model of conciseness and logic, ideally suited to the needs of both students and research workers in physics and chemistry.
Based on Planck's original papers, the book offers a uniform point of view for the entire field. Rejecting the earlier approaches of Helmholtz and Maxwell, Planck makes no assumptions regarding the nature of heat, but begins with only a few empirical facts from which he deduces new physical and chemical laws. He considers fundamental facts and definitions (temperature, molecular weight, quantity of heat), the first and second fundamental principles of thermodynamics (applications to homogeneous and non-homogeneous systems, proof, general deductions), and applications to special states of equilibrium (homogeneous systems, systems in various states of aggregation, system of any number of independent constituents, gaseous systems, dilute solutions, absolute value of the entropy, Nernst's theorem). Throughout the book numerous examples are worked.
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Quantum Mechanics
Principles and Formalism
by Roy McWeeny
Part of the Dover Books on Physics series
Concerned strictly with the principles and formalism of quantum mechanics, this graduate student-oriented volume develops the subject as a fundamental discipline. Opening chapters review the origins of Schrödinger's equations and the nature of the solutions in certain simple and well-known cases, advancing to the ideas associated with vector spaces. Having provided students with the appropriate mathematical language, the author proceeds to the formulation of the main principles of quantum mechanics and their immediate consequences. The book concludes with final generalizations in which alternative "languages" or representations are discussed - each with reference to its specific advantages and applications - and the Dirac transformation theory is developed and explained.
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Axiomatics of Classical Statistical Mechanics
by Rudolf Kurth
Part of the Dover Books on Physics series
Requiring only familiarity with elements of calculus and analytical geometry, this monograph constructs classical statistical mechanics as a deductive system, based on equations of motion and basic postulates of probability. 1960 edition.
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Special Relativity for Physicists
by G. Stephenson
Part of the Dover Books on Physics series
This concise account of special relativity is geared toward nonspecialists and belongs in the library of anyone interested in the subject and its applications to both classical and modern physics. The treatment takes a historical point of view, without making heavy demands on readers' mathematical abilities; in fact, the theory is developed without the use of tensor calculus, requiring only a working knowledge of three-dimensional vector analysis. Topics include detailed coverage of the Lorentz transformation, including optical and dynamical applications, and applications to modern physics. An excellent bibliography completes this compact, accessible presentation.
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Water Waves
The Mathematical Theory with Applications
by James Johnston Stoker
Part of the Dover Books on Physics series
First published in 1957, this is a classic monograph in the area of applied mathematics. It offers a connected account of the mathematical theory of wave motion in a liquid with a free surface and subjected to gravitational and other forces, together with applications to a wide variety of concrete physical problems. A never-surpassed text, it remains of permanent value to a wide range of scientists and engineers concerned with problems in fluid mechanics.
The four-part treatment begins with a presentation of the derivation of the basic hydrodynamic theory for non-viscous incompressible fluids and a description of the two principal approximate theories that form the basis for the rest of the book. The second section centers on the approximate theory that results from small-amplitude wave motions. A consideration of problems involving waves in shallow water follows, and the text concludes with a selection of problems solved in terms of the exact theory. Despite the diversity of its topics, this text offers a unified, readable, and largely self-contained treatment.
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Unsteady Transonic Flow
by Marten T. Landahl
Part of the Dover Books on Physics series
This classic monograph on unsteady transonic flow - the flow of air encountered at speeds at or near the speed of sound - is of continuing interest to students and professionals in aerodynamics, fluid dynamics, and other areas of applied mathematics.
After a brief Introduction, Swedish physicist Mårten T. Landahl presents a chapter in which the two-dimensional solution is derived, succeeded by a discussion of its relation to the subsonic and supersonic solutions. Three chapters on low aspect ratio configurations follow, covering triangular wings and similar planforms with curved leading edges, rectangular wings, and cropped delta wings, and low aspect ratio wing-body combinations. The treatment concludes with a consideration of the experimental determination of air forces on oscillating wings at transonic speeds.
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Nonequilibrium Statistical Thermodynamics
by Bernard H. Lavenda
Part of the Dover Books on Physics series
This book develops in detail the statistical foundations of nonequilibrium thermodynamics, based on the mathematical theory of Brownian motion. Author Bernard H. Lavenda demonstrates that thermodynamic criteria emerge in the limit of small thermal fluctuations and in the Gaussian limit where means and modes of the distribution coincide. His treatment assumes the theory of Brownian motion to be a general and practical model of irreversible processes that are inevitably influenced by random thermal fluctuations. This unifying approach permits the extraction of widely applicable principles from the analysis of specific models.
Arranged by argument rather than theory, the text is based on the premises that random thermal fluctuations play a decisive role in governing the evolution of nonequilibrium thermodynamic processes and that they can be viewed as a dynamic superposition of many random events. Intended for nonmathematicians working in the areas of nonequilibrium thermodynamics and statistical mechanics, this book will also be of interest to chemical physicists, condensed matter physicists, and readers in the area of nonlinear optics.
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Solved Problems in Classical Electromagnetism
by Jerrold Franklin
Part of the Dover Books on Physics series
Solved Problems in Classical Electromagnetism is a valuable tool to help students learn to do physics while using concepts they learn in the courses. Students who are taking or have already taken an advanced EM course will find the book to be a useful adjunct to their textbook, giving added practice in applying what they are learning. For students who are taking an undergraduate EM course and want to get more depth, this book can help them achieve that aim and also help them prepare for graduate work. Beginning students, or those not even taking a course at the moment, can benefit from these problems and learn just from working on them with the help of the solutions. In each chapter, the problems start out relatively easy and then get progressively more advanced, helping students to go just as far as they can at their present level. The book includes a number of review sections to assist students without previous advanced training in working out the problems. The first review section is a comprehensive development of vector calculus that will prepare students to solve the problems and provide a strong foundation for their future development as physicists. The problems are drawn from the topics of electrostatics, magnetostatics, Maxwell's equations, electromagnetic radiation, and relativisitc electromagnetism.
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Perturbation Theory and the Nuclear Many Body Problem
by Kailash Kumar
Part of the Dover Books on Physics series
This introductory treatment begins with an overview of the basic ideas of perturbation theory, addressing the conditions under which the theory may be set up and the various forms of perturbation expansions. Subsequent chapters explore diagrammatic methods in terms of linked cluster theorem and general formulas as well as rearrangement methods. Techniques of solving the t-matrix equation and other equations that arise in the nuclear many body problem are examined in terms of approximate methods, and the intuitive reasoning behind each of them is given. The text's final chapter collects other methods of approaching the many body problem and shows how they may be compared with those of previous chapters. Suitable for advanced undergraduates and graduate students, this volume features many helpful citations to literature on the subject, and a list of main symbols has been appended to each chapter for easy reference.
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Operators and Representation Theory
Canonical Models for Algebras of Operators Arising in Quantum Mechanics
by Palle E.T. Jorgensen
Part of the Dover Books on Physics series
Suitable for advanced undergraduates and graduate students in mathematics and physics, this three-part treatment of operators and representation theory begins with background material on definitions and terminology as well as on operators in Hilbert space. The introductory section concludes with a look at the imprimitivity theorem, which grounds in more mathematical language the work of Wigner on representations of the Poincaré and Galilei groups. The second part of the monograph addresses the algebras of operators in Hilbert space, broadening the mathematics used in earlier versions of quantum theory. There are many examples in which the Hamiltonian, the operator that translates a quantum system in time, can be written as a polynomial in elements of an underlying Lie algebra. This section deals with properties of such operators. Part 3 explores covariant representation and connections, with a particular focus on infinite-dimensional Lie algebras. Connections to mathematical physics are stressed throughout the text, which concludes with three helpful appendixes, including a Guide to the Literature.
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Mathematical Aspects of Subsonic and Transonic Gas Dynamics
by Lipman Bers
Part of the Dover Books on Physics series
This concise volume by a prominent mathematician offers an important survey of mathematical aspects of the theory of compressible fluids. The treatment is geared toward advanced undergraduates and graduate students in physics, applied mathematics, and engineering. Focusing on two-dimensional steady potential flows, the text eschews detailed proofs in favor of clear indications of the main ideas and descriptions of new mathematical concepts and methods that arose in connection with these chapters in fluid dynamics. Starting with a general discussion of the differential equations of a compressible gas flow, the book advances to the mathematical background of subsonic flow theory. Subsequent chapters explore the behavior of a flow at infinity and methods for the determination of flows around profiles, flows in channels and with a free boundary, the mathematical background of transonic gas dynamics, and some problems in transonic flow. An extensive bibliography of 400 papers concludes the text.
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Continuum Mechanics
Concise Theory and Problems
by P. Chadwick
Part of the Dover Books on Physics series
Written in response to the dearth of practical and meaningful textbooks in the field of fundamental continuum mechanics, this comprehensive treatment offers students and instructors an immensely useful tool. Its 115 solved problems and exercises not only provide essential practice but also systematically advance the understanding of vector and tensor theory, basic kinematics, balance laws, field equations, jump conditions, and constitutive equations. Readers follow clear, formally precise steps through the central ideas of classical and modern continuum mechanics, expressed in a common, efficient notation that fosters quick comprehension and renders these concepts familiar when they reappear in other contexts. Completion of this brief course results in a unified basis for work in fluid dynamics and the mechanics of solid materials, a foundation of particular value to students of mathematics and physics, those studying continuum mechanics at an intermediate or advanced level, and postgraduate students in the applied sciences.
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Symmetry
An Introduction to Group Theory and Its Applications
by Roy McWeeny
Part of the Dover Books on Physics series
This well-organized volume develops the elementary ideas of both group theory and representation theory in a progressive and thorough fashion. Designed to allow students to focus on any of the main fields of application, it is geared toward advanced undergraduate and graduate physics and chemistry students. 1963 edition. Appendices.
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Solid State Theory
by Walter A. Harrison
Part of the Dover Books on Physics series
This excellent text, ideal for a one-year course in solid state theory, covers electron states, electronic properties of solids, lattice vibrations and atomic properties, the Mott transition, the electronic structure of disordered systems, tunneling, the Kond effect, the fluctuation near critical points, and more.
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Introduction to Electromagnetic Theory
by George E. Owen
Part of the Dover Books on Physics series
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.
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Quantum Mechanics
New Approaches to Selected Topics
by Harry J. Lipkin
Part of the Dover Books on Physics series
This collection of self-contained studies is geared toward advanced undergraduates and graduate students. Its broad selection of topics includes the Mössbauer effect, many-body quantum mechanics, scattering theory, Feynman diagrams, and relativistic quantum mechanics. Author Harry J. Lipkin, a well-known teacher at Israel's Weizmann Institute, takes an unusual approach by introducing many interesting physical problems and mathematical techniques at a much earlier point than in conventional texts. This method enables students to observe the physical implications and useful applications of quantum theory before mastering the formalism in detail, and it provides them with new mathematical tools at an earlier stage for use in subsequent problems.
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Selected Problems in Physics with Answers
by M. P. Shaskol'skaya
Part of the Dover Books on Physics series
Intended as supplementary material for undergraduate physics students, this wide-ranging collection of problems in applied mathematics and physics features complete solutions. Topics include kinematics; dynamics of motion in a straight line; statics; laws of conservation; dynamics of motion in a circle; universal theory of gravitation; oscillation, waves, and sound; and more.
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Quantum Field Theory
by Claude Itzykson
Part of the Dover Books on Physics series
Quantum field theory remains among the most important tools in defining and explaining the microscopic world. Recent years have witnessed a blossoming of developments and applications that extend far beyond the theory's original scope. This comprehensive text offers a balanced treatment, providing students with both a formal presentation and numerous practical examples of calculations. This two-part approach begins with the standard quantization of electrodynamics, culminating in the perturbative renormalization. The second part comprises functional methods, relativistic bound states, broken symmetries, nonabelian gauge fields, and asymptotic behavior. Appropriate for students and researchers in field theory, particle physics, and related areas, this treatment presupposes a background in quantum mechanics, electrodynamics, and relativity, and it assumes some familiarity with classical calculus, including group theory and complex analysis.
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Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena
by Ya. B. Zel'dovich
Part of the Dover Books on Physics series
Physical, chemical processes in gases at high temperatures are focus of outstanding text by two distinguished physicists. Combines material from gas dynamics, shock-wave theory, thermodynamics and statistical physics, molecular physics, spectroscopy, radiation theory, other fields for comprehensive treatment. 284 black-and-white illustrations. 1966–1967 edition, originally published in two volumes.
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Elasticity
by Robert William Soutas-Little
Part of the Dover Books on Physics series
According to the author, elasticity may be viewed in many ways. For some, it is a dusty, classical subject . . . to others it is the paradise of mathematics." But, he concludes, the subject of elasticity is really "an entity itself," a unified subject deserving comprehensive treatment. He gives elasticity that full treatment in this valuable and instructive text. In his preface, Soutas-Little offers a brief survey of the development of the theory of elasticity, the major mathematical formulation of which was developed in the 19th century after the first concept was proposed by Robert Hooke in 1678. The theory was further refined in the 20th century as a means of solving the equations presented earlier. The book is divided into three major sections. The first section presents a review of mathematical notation and continuum mechanics, covering vectors and tensors, kinematics, stress, basic equations of continuum mechanics, and linear elasticity. The second section, on two-dimensional elasticity, treats the general theory of plane elasticity, problems in Cartesian coordinates, problems in polar coordinates, complex variable solutions, finite difference and finite element methods, and energy theorems and variational techniques. Section three discusses three-dimensional problems, and is devoted to Saint Venant torsion and bending theory, the Navier equation and the Galerkin vector, and the Papkovich-Neuber solution. Numerous illustrative figures and tables appear throughout the book, and valuable reference material is provided in the appendices on eigenfunction analysis, trigonometric functions, Fourier transforms, inverse transforms, complex variable formulae, Hankel transforms, and Bessel and Legendre functions. Instructors will find this an ideal text for a two-course sequence in elasticity; they can also use it as a basic introduction to the subject by selecting appropriate sections of each part.