Dover Books on Physics
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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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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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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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Space, Time, Matter
by Hermann Weyl
Part of the Dover Books on Physics series
Long one of the standard texts in the field, this excellent introduction probes deeply into Euclidean space, Riemann's space, Einstein's general relativity, gravitational waves and energy, and laws of conservation.
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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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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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Quantum Mechanics With Applications
by David B. Beard
Part of the Dover Books on Physics series
This introductory text emphasizes Feynman's development of path integrals and its application to wave theory for particles. Suitable for undergraduate and graduate students of physics, the well-written, clear, and rigorous text was written by two of the nation's leading authorities on quantum physics. A solid foundation in quantum mechanics and atomic physics is assumed. Early chapters provide background in the mathematical treatment and particular properties of ordinary wave motion that also apply to particle motion. The close relation of quantum theory to physical optics is stressed. Subsequent sections emphasize the physical consequences of a wave theory of material properties, and they offer extensive applications in atomic physics, nuclear physics, solid state physics, and diatomic molecules. Four helpful Appendixes supplement the text.
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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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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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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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Classical Electromagnetic Radiation, Third Edition
by Mark A. Heald
Part of the Dover Books on Physics series
Newly corrected, this edition of a highly acclaimed text is suitable for advanced physics courses. Its accessible macroscopic view of classical electromagnetics emphasizes integrating electromagnetic theory with physical optics. 1995 edition.
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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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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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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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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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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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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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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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Fundamental Formulas of Physics, Volume One
by Donald H. Menzel
Part of the Dover Books on Physics series
Volume 1 of a two-volume set. This important work covers basic mathematical formulas, statistics, nomograms, physical constants, classical mechanics, special theory of relativity, general theory of relativity, hydrodynamics and aerodynamics, boundary value problems in mathematical physics, heat and thermodynamics, statistical mechanics, kinetic theory of gases, viscosity, thermal conductions, electromagnetism, electronics and much more.
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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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Statistical Mechanics
Principles and Selected Applications
by Terrell L. Hill
Part of the Dover Books on Physics series
Standard text opens with clear, concise chapters on classical statistical mechanics, quantum statistical mechanics, and the relation of statistical mechanics to thermodynamics. Further topics cover fluctuations, the theory of imperfect gases and condensation, distribution functions and the liquid state, nearest neighbor (Ising) lattice statistics, and more.
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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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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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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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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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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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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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A Guide to Feynman Diagrams in the Many-Body Problem
by Richard D. Mattuck
Part of the Dover Books on Physics series
Until this book, most treatments of this topic were inaccessible to nonspecialists. A superb introduction to important areas of modern physics, it covers Feynman diagrams, quasi particles, Fermi systems at finite temperature, superconductivity, vacuum amplitude, Dyson's equation, ladder approximation, and much more.
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States of Matter
by David L. Goodstein
Part of the Dover Books on Physics series
This unique overview by a prominent CalTech physicist provides a modern, rigorous, and integrated treatment of the key physical principles and techniques related to gases, liquids, solids, and their phase transitions. No other single volume offers such comprehensive coverage of the subject, and the treatment consistently emphasizes areas in which research results are likely to be applicable to other disciples. Starting with a chapter on thermodynamics and statistical mechanics, the text proceeds to in-depth discussions of perfect gases, electrons in metals, Bose condensation, fluid structure, potential energy, Weiss molecular field theory, van der Waals equation, and other pertinent aspects of phase transitions. Many helpful illustrative problems appear at the end of each chapter, and annotated bibliographies offer further guidance.
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Introduction to Modern Optics
by Grant R. Fowles
Part of the Dover Books on Physics series
This incisive text provides a basic undergraduate-level course in modern optics for students in physics, technology and engineering. The first half of the book deals with classical physical optics; the second principally with the quantum nature of light. Chapters 1 and 2 treat the propagation of light waves, including the concepts of phase and group velocities, and the vectorial nature of light. Chapter 3 applies the concepts of partial coherence and coherence length to the study of interference, and Chapter 4 takes up multiple-beam interference and includes Fabry-Perot interferometry and multilayer-film theory. Diffraction and holography are the subjects of Chapter 5, and the propagation of light in material media (including crystal and nonlinear optics) are central to Chapter 6. Chapters 7 and 8 introduce the quantum theory of light and elementary optical spectra, and Chapter 9 explores the theory of light amplification and lasers. Chapter 10 briefly outlines ray optics in order to introduce students to the matrix method for treating optical systems and to apply the ray matrix to the study of laser resonators. Many applications of the laser to the study of optics are integrated throughout the text. The author assumes students have had an intermediate course in electricity and magnetism and some advanced mathematics beyond calculus. For classroom use, a list of problems is included at the end of each chapter, with selected answers at the end of the book.
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Understanding Thermodynamics
by H. C. Van Ness
Part of the Dover Books on Physics series
Clearly written treament elucidates fundamental concepts and demonstrates their plausibility and usefulness. Language is informal, examples are vivid and lively, and the perspectivie is fresh. Based on lectures delivered to engineering students, this work will also be valued by scientists, engineers, technicians, businessmen, anyone facing energy challenges of the future.
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Introduction to Mathematical Fluid Dynamics
by Richard E. Meyer
Part of the Dover Books on Physics series
Fluid dynamics, the behavior of liquids and gases, is a field of broad impact that encompasses aspects of physics, engineering, oceanography, and meteorology. Full understanding demands fluency in higher mathematics, the only language of fluid dynamics. This introductory text is geared toward advanced undergraduate and graduate students in applied mathematics, engineering, and the physical sciences. It assumes a knowledge of calculus and vector analysis. Author Richard E. Meyer notes, "This core of knowledge concerns the relation between inviscid and viscous fluids, and the bulk of this book is devoted to a discussion of that relation." Dr. Meyer develops basic concepts from a semi-axiomatic foundation, observing that such treatment helps dispel the common impression that the entire subject is built on a quicksand of assorted intuitions. His topics include kinematics, momentum principle and ideal fluid, Newtonian fluid, fluids of small viscosity, some aspects of rotating fluids, and some effects of compressibility. Each chapter concludes with a set of problems.
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Optical Processes in Semiconductors
by Jacques I. Pankove
Part of the Dover Books on Physics series
This comprehensive textbook and reference covers all phenomena involving light in semiconductors, emphasizing modern applications in semiconductor lasers, electroluminescence, photodetectors, photoconductors, photoemitters, polarization effects, absorption spectroscopy, radiative transfers and reflectance modulatons. With numerous problems. 339 illustrations.
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Mathematics of Classical and Quantum Physics
by Frederick W. Byron
Part of the Dover Books on Physics series
Well-organized text designed to complement graduate-level physics texts in classical mechanics, electricity, magnetism, and quantum mechanics. Topics include theory of vector spaces, analytic function theory, Green's function method of solving differential and partial differential equations, theory of groups, more. Many problems, suggestions for further reading.
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An Elementary Treatise on Electricity
by James Clerk Maxwell
Part of the Dover Books on Physics series
Albert Einstein characterized the work of James Clerk Maxwell as the "most profound and the most fruitful that physics has experienced since the time of Newton." Max Planck went even further, declaring that "he achieved greatness unequalled," and Richard Feynman asserted that "From a long view of the history of mankind - seen from, say, ten thousand years from now - there can be little doubt that the most significant event of the nineteenth century will be judged as Maxwell's discovery of the laws of electrodynamics." Maxwell made numerous other contributions to the advancement of science, but the greatest work of his life was devoted to electricity. An Elementary Treatise on Electricity appeared at a time when very few books on electrical measurements were available to students, and its compact treatment not only elucidates the theory of electricity but also serves to develop electrical ideas in readers' minds. The author describes experiments that demonstrate the principal facts relating an electric charge as a quantity capable of being measured, deductions from these facts, and the exhibition of electrical phenomena. This volume, published posthumously from Maxwell's lecture notes at the Cavendish Laboratory - which he founded at the University of Cambridge - is supplemented by a selection of articles from his landmark book, Electricity and Magnetism. A classic of science, this volume is an eminently suitable text for upper-level undergraduates and graduate students.
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Group Theory in Quantum Mechanics
An Introduction to Its Present Usage
by Volker Heine
Part of the Dover Books on Physics series
Geared toward research students in physics and chemistry, this text introduces the three main uses of group theory in quantum mechanics: (1) to label energy levels and the corresponding eigenstates; (2) to discuss qualitatively the splitting of energy levels, starting from an approximate Hamiltonian and adding correction terms; and (3) to aid in the evaluation of matrix elements of all kinds. "The theme," states author Volker Heine, "is to show how all this is achieved by considering the symmetry properties of the Hamiltonian and the way in which these symmetries are reflected in the wave functions." Early chapters cover symmetry transformations, the quantum theory of a free atom, and the representations of finite groups. Subsequent chapters address the structure and vibrations of molecules, solid state physics, nuclear physics, and relativistic quantum mechanics. A previous course in quantum theory is necessary, but the relevant matrix algebra appears in an appendix. A series of examples of varying levels of difficulty follows each chapter. They include simple drills related to preceding material as well as extensions of theory and further applications. The text is enhanced with 46 illustrations and 12 helpful appendixes.
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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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Techniques and Applications of Path Integration
by L. S. Schulman
Part of the Dover Books on Physics series
A book of techniques and applications, this text defines the path integral and illustrates its uses by example. It is suitable for advanced undergraduates and graduate students in physics; its sole prerequisite is a first course in quantum mechanics. For applications requiring specialized knowledge, the author supplies background material. The first part of the book develops the techniques of path integration. Topics include probability amplitudes for paths and the correspondence limit for the path integral; vector potentials; the Ito integral and gauge transformations; free particle and quadratic Lagrangians; properties of Green's functions and the Feynman-Kac formula; functional derivatives and commutation relations; Brownian motion and the Wiener integral; and perturbation theory and Feynman diagrams. The second part, dealing with applications, covers asymptotic analysis and the calculus of variations; the WKB approximation and near caustics; the phase of the semiclassical amplitude; scattering theory; and geometrical optics. Additional topics include the polaron; path integrals for multiply connected spaces; quantum mechanics on curved spaces; relativistic propagators and black holes; applications to statistical mechanics; systems with random impurities; instantons and metastability; renormalization and scaling for critical phenomena; and the phase space path integral.
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Foundations of Laser Spectroscopy
by Stig Stenholm
Part of the Dover Books on Physics series
One of the first texts to offer a simple presentation of the theoretical foundations of steady-state laser spectroscopy, this volume is geared toward beginning theorists and experimentalists. It assists students in applying theoretical ideas to actual calculations in laser spectroscopy with a systematic series of examples and exercises. Starting at an elementary level, students gradually build up their practical skills with demonstrations of how simplified theoretical models relate to experimentally observable quantities. Detailed derivations offer students the opportunity to work out all results for themselves. The first chapter introduces background material on electrodynamics and quantum mechanics, with an emphasis on the density matrix, its equation of motion, and its interpretation. Chapter 2 derives the response of the medium to strong fields. After mastering these two parts, students can proceed to later chapters in any order they wish. Succeeding chapters cover the physical basis of laser operation, applications central to laser spectroscopy, the inclusion of laser fluctuations into the theory, and field quantization. Numerous references, which appear in separate sections, form a concise history of the field and its most noteworthy developments.
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Boundary and Eigenvalue Problems in Mathematical Physics
by Hans Sagan
Part of the Dover Books on Physics series
This well-known text uses a limited number of basic concepts and techniques - Hamilton's principle, the theory of the first variation and Bernoulli's separation method - to develop complete solutions to linear boundary value problems associated with second order partial differential equations such as the problems of the vibrating string, the vibrating membrane, and heat conduction. It is directed to advanced undergraduate and beginning graduate students in mathematics, applied mathematics, physics, and engineering who have completed a course in advanced calculus. In the first three chapters, Professor Sagan introduces Hamilton's principle and the theory of the first variation; he then discusses the representation of the vibrating string, the vibrating membrane and heat conduction (without convection) by partial differential equations. Bernoulli's separation method and infinite series solutions of homogeneous boundary value problems are introduced as a means for solving these problems. The next three chapters take up Fourier series, self-adjoint boundary value problems, Legendre polynomials, and Bessel functions. The concluding three chapters address the characterization of eigenvalues by a variational principle; spherical harmonics, and the solution of the Schroedinger equation for the hydrogen atom; and the nonhomogeneous boundary value problem. Professor Sagan concludes most sections of this excellent text with selected problems (solutions provided for even-numbered problems) to reinforce the reader's grasp of the theories and techniques presented.
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Dynamic Light Scattering
With Applications to Chemistry, Biology, and Physics
by Bruce J. Berne
Part of the Dover Books on Physics series
Lasers play an increasingly important role in a variety of detection techniques, making inelastic light scattering a tool of growing value in the investigation of dynamic and structural problems in chemistry, biology, and physics. Until the initial publication of this work, however, no monograph treated the principles behind current developments in the field.This volume presents a comprehensive introduction to the principles underlying laser light scattering, focusing on the time dependence of fluctuations in fluid systems; it also serves as an introduction to the theory of time correlation functions, with chapters on projection operator techniques in statistical mechanics. The first half comprises most of the material necessary for an elementary understanding of the applications to the study of macromolecules, or comparable sized particles in fluids, and to the motility of microorganisms. The study of collective (or many particle) effects constitutes the second half, including more sophisticated treatments of macromolecules in solution and most of the applications of light scattering to the study of fluids containing small molecules.With its wide-ranging discussions of the many applications of light scattering, this text will be of interest to research chemists, physicists, biologists, medical and fluid mechanics researchers, engineers, and graduate students in these areas.
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An Introduction to Acoustics
by Robert H. Randall
Part of the Dover Books on Physics series
No branch of classical physics is older in its origins yet more modern in its applications than acoustics. Courses on acoustics very naturally begin with a study of vibrations, as a preliminary to the introduction of the wave equations. Both vibrations and waves, of course, are vastly important to all branches of physics and engineering. But it is very helpful to students to gain an understanding of mechanical waves before trying to comprehend the more subtle and abstract electromagnetic ones. This undergraduate-level text opens with an overview of fundamental particle vibration theory, and it proceeds to examinations of waves in air and in three dimensions, interference patterns and diffraction, and acoustic impedance, as illustrated in the behavior of horns. Subsequent topics include longitudinal waves in different gases and waves in liquids and solids; stationary waves and vibrating sources, as demonstrated by musical instruments; reflection and absorption of sound waves; speech and hearing; sound measurements and experimental acoustics; reproduction of sound; and miscellaneous applied acoustics. Supplementary sections include four appendixes and answers to problems. Introduction. Appendixes. List of Symbols. References. Index. Answers to Problems.
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Nonlinear Dynamics
Exploration Through Normal Forms
by Yair Zarmi
Part of the Dover Books on Physics series
Geared toward advanced undergraduates and graduate students, this exposition covers the method of normal forms and its application to ordinary differential equations through perturbation analysis. In addition to its emphasis on the freedom inherent in the normal form expansion, the text features numerous examples of equations, the kind of which are encountered in many areas of science and engineering. The treatment begins with an introduction to the basic concepts underlying the normal forms. Coverage then shifts to an investigation of systems with one degree of freedom that model oscillations, in which the force has a dominant linear term and a small nonlinear one. The text considers a variety of nonautonomous systems that arise during the study of forced oscillatory motion. Topics include boundary value problems, connections to the method of the center manifold, linear and nonlinear Mathieu equations, pendula, Nuclear Magnetic Resonance, coupled oscillator systems, and other subjects. 1998 edition.
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Theoretical Nuclear Physics
by John M. Blatt
Part of the Dover Books on Physics series
An uncommonly clear and cogent investigation and correlation of key aspects of theoretical nuclear physics by leading experts: the nucleus, nuclear forces, nuclear spectroscopy, two-, three- and four-body problems, nuclear reactions, beta-decay and nuclear shell structure. Directed to the experimental physicist working in nuclear physics or graduate students who know the essential concepts and problems. 112 illustrations.
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Introduction to Quantum Mechanics with Applications to Chemistry
by Linus Pauling
Part of the Dover Books on Physics series
When this classic text was first published in 1935, it fulfilled the goal of its authors "to produce a textbook of practical quantum mechanics for the chemist, the experimental physicist, and the beginning student of theoretical physics." Although many who are teachers today once worked with the book as students, the text is still as valuable for the same undergraduate audience. Two-time Nobel Prize winner Linus Pauling, Research Professor at the Linus Pauling Institute of Science and Medicine, Palo Alto, California, and E. Bright Wilson, Jr., Professor Emeritus of Chemistry at Harvard University, provide a readily understandable study of "wave mechanics," discussing the Schrodinger wave equation and the problems which can be solved with it. Extensive knowledge of mathematics is not required, although the student must have a grasp of elementary mathematics through the calculus. Pauling and Wilson begin with a survey of classical mechanics, including Newton's equations of motion in the Lagrangian form, and then move on to the "old" quantum theory, developed through the work of Planck, Einstein and Bohr. This analysis leads to the heart of the book ― an explanation of quantum mechanics which, as Schrodinger formulated it, "involves the renunciation of the hope of describing in exact detail the behavior of a system." Physics had created a new realm in which classical, Newtonian certainties were replaced by probabilities ― a change which Heisenberg's uncertainty principle (described in this book) subsequently reinforced. With clarity and precision, the authors guide the student from topic to topic, covering such subjects as the wave functions for the hydrogen atom, perturbation theory, the Pauli exclusion principle, the structure of simple and complex molecules, Van der Waals forces, and systems in thermodynamic equilibrium. To insure that the student can follow the mathematical derivations, Pauling and Wilson avoid the "temptation to condense the various discussions into shorter and perhaps more elegant forms" appropriate for a more advanced audience. Introduction to Quantum Mechanics is a perfect vehicle for demonstrating the practical application of quantum mechanics to a broad spectrum of chemical and physical problems.
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X-Ray Diffraction
by B. E. Warren
Part of the Dover Books on Physics series
This rigorous graduate-level introduction stresses modern applications to nonstructural problems such as temperature vibration effects, order-disorder phenomena, crystal imperfections, the structure of amorphous materials, and the diffraction of x-rays in perfect crystals. Relevant problems at chapter ends. Six Appendixes include tables of values. Bibliographies. 146 illustrations.
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Mathematical Foundations of Quantum Mechanics
by George W. Mackey
Part of the Dover Books on Physics series
Designed for students familiar with abstract mathematical concepts but possessing little knowledge of physics, this text focuses on generality and careful formulation rather than problem-solving. Its author, a member of the distinguished National Academy of Science, based this graduate-level text on the course he taught at Harvard University. Opening chapters on classical mechanics examine the laws of particle mechanics; generalized coordinates and differentiable manifolds; oscillations, waves, and Hilbert space; and statistical mechanics. A survey of quantum mechanics covers the old quantum theory; the quantum-mechanical substitute for phase space; quantum dynamics and the Schrödinger equation; the canonical "quantization" of a classical system; some elementary examples and original discoveries by Schrödinger and Heisenberg; generalized coordinates; linear systems and the quantization of the electromagnetic field; and quantum-statistical mechanics. The final section on group theory and quantum mechanics of the atom explores basic notions in the theory of group representations; perturbations and the group theoretical classification of eigenvalues; spherical symmetry and spin; and the n-electron atom and the Pauli exclusion principle.