Theoretical Physics

782 Pages·1987·34.88 MB·English

by  Georg Joos

Theoretical Physics
Theoretical Physics
GEORG JOOS
Professor of Experimental Physics at the
Technische Hochschule, Munich
With the Collaboration of
IRA M. FREEMAN
Professor of Physics, Rutgers University
THIRD EDITION
Dover Publications, Inc., New York
This Dover edition, first published in 1986, is an unabridged republication of the third edition (1958) of the work first published by Blackie
and Son, Ltd., Glasgow, Scotland, in 1934.
Library of Congress Cataloging-in-Publication Data
Joos, Georg, 1894-1959.
Theoretical physics.
Translation of: Lehrbuch der theoretischen Physik.
Reprint. Originally published: 3rd ed. London : Blackie & Son, Ltd.; New York: Hafner Pub. Co., 1958.
Bibliography: p.
Includes index.
1. Mathematical physics. I. Freeman, Ira Maximilian, 1905- .II. Title.
QC20.J613 1986 530.1 86-29083
ISBN-13: 978-0-486-65227-6 (pbk.)
ISBN-10: 0-486-65227-0 (pbk.)
Manufactured in the United States by Courier Corporation
65227011
www.doverpublications.com
PREFACE TO THE SECOND EDITION
FROM its inception, the aim of this book has been to bring the reader to an intermediate level of
attainment in the main branches of theoretical physics from which he may be able to proceed, with the
help of special literature, to the field of research. Experience shows that it is often the first contact with a
complex problem that presents the major difficulty, and it is here that help is most urgently needed.
Nevertheless, it is necessary to make a certain selection from the many topics that seem to offer promise
of development. For example, there is the question of whether an extensive treatment of the
HamiltonJacobi mechanics, which at the time of the first edition (1932) formed the basis of the old atom
theory, is still advisable. The decision to retain it is founded on the conviction that only in this way is the
compelling and logical evolution of atomic physics in the form of wave mechanics clearly seen.
Ensuing revisions of the book have made possible the recasting of the presentation of many topics. The
subject of nuclear physics required, of course, the most extensive changes. In this connexion it is felt that a
concise survey of the main lines of cosmic ray research is now in order, since knowledge in this field has
progressed far beyond the stage of mere speculation. In this brief presentation much of the great mass of
experimental material has been omitted, and it is hoped that specialists in this field will not be too critical
of what is apparently a somewhat oversimplified picture. Geometric optics has been given more space
and the theory of the top has been modernized on the basis of a treatment suggested by Professor
Bauersfeld.
The range of subject matter has been extended by the inclusion of selected topics in what might be
called “ applied theoretical physics ”. To have included these items in the respective chapters dealing
with these subjects would have interrupted the continuity of development, and so they have been grouped
in a separate Part of the book. In response to numerous suggestions, a Mathematical Addendum on the
properties of Bessel Functions and Spherical Harmonics has been prepared. This material has been
placed intentionally at the end of the work rather than in the Mathematical Introduction, in as much as it
demands a somewhat higher order of computational skill on the part of the reader.
Other changes include: (a) introduction of the M.K.S. system, chiefly in the formulas of macroscopic
electromagnetism (there is no reason to change the familiar numerical relations in atomic physics); (b)
addition of a considerable number of new exercises; (c) revision of the numerical values of physical
constants; and (d) extension of the list of references for further study. It is hoped that these alterations will
increase the usefulness of the work in its dual role of text and reference book.
G. J.
I. M. F.
BOSTON, MASS., AND
NEW BRUNSWICK, N.J.,
U.S.A.
April, 1950.
PREFACE TO THE THIRD EDITION
In this revision there are two additional chapters: (1) Phenomenological Theory of Superconductivity,
(2) Theory of Elastomers; and the chapter on Nuclear Physics is considerably modified. A section on
Fundamentals of the Matrix Calculus has been added to the first chapter and one on The Role of Lattice
Defects in Dielectric Crystals to Chapter XLI. The Table of Physical Constants has also been revised.

CONTENTS
Sections marked with an asterisk are somewhat more difficult
and may be omitted in the first perusal of the work
PART I
MATHEMATICAL INTRODUCTION
CHAPTER I
Vector Analysis
1. The Concept of a Vector
2. Addition and Subtraction of Vectors; Multiplication of a Vector by a Scalar
3. The Scalar Product of two Vectors
4. The Vector Product of two Vectors. The directed Plane Area as a Vector
5. Multiple Products
6. Differentiation of a Vector with respect to a Scalar; Application to the Theory of Space Curves
7. Space Derivatives of a Scalar Quantity
8. The Concept of Divergence and Gauss’s Theorem
9. The Curl of a Vector, and Stokes’s Theorem
10. The Operator ∇
11. Calculation of the Gradient in a Vector Field; Fundamental Principles of Tensor Analysis
12. Calculation of more complicated Vector Differential Expressions with the help of the Nabla
Operator
13. Differential Vector Operations in Curvilinear Orthogonal Co-ordinates
14. Degeneration of the Vector Differential Operations at Surfaces of Discontinuity in the Field
15. Fundamentals of the Matrix Calculus
CHAPTER II
Mathematical Representation of Periodic
Phenomena; Theory of Vibrations and Waves
1. Simple Harmonic Vibrations
2. Representation of more complicated Periodic Phenomena by Series of Harmonic Terms. Fourier
Series. The Fourier Integral
3. Modulated Vibrations and Beats
4. Combination of Vibrations along different Axes. Lissajous’ Figures
5. The Propagation of Periodic Disturbances in the form of Waves
6. Combination of several Waves having the same Direction of Propagation; Linearly and Elliptically
Polarized Waves; Group Velocity
7. Combination of Waves having the same Frequency but different Directions of Propagation. Standing
Waves
CHAPTER III
Selected Topics in the Theory of Functions
of a Complex Variable
1. Conformal Mapping of one Plane on another
2. The Cauchy-Riemann Conditions and the Differential Equation of Laplace
3. Line Integrals in the Gauss Plane; the Cauchy Integral Theorem
CHAPTER IV
The Fundamental Problem
of the Calculus of Variations and its Solution
1. Statement of the Problem of the Calculus of Variations
2. Derivation of the Euler-Lagrange Differential Equation
PART II
MECHANICS
CHAPTER V
The Mechanics of a Single Particle
1. The Fundamental Concepts of Kinematics
2. Newton’s Second Law of Motion
3. Time Integral and Path Integral of the Force. Work and Energy
4. Conservative Forces; Potential
5. Central Forces; the Law of Areas
6. Gravitational Forces; Planetary Motion
7. Quasi-elastic Forces and Harmonic Vibrations
8. Harmonic Vibrations with Frictional Resistance
9. Forced Vibrations; Resonance
10. Non-harmonic Vibrations; Sudden Changes of Amplitude
11. Mechanics of a Constrained Particle. The Simple Pendulum
CHAPTER VI
General Theorems on the Mechanics
of Systems of Particles
1. Theorem concerning the Motion of the Centre of Mass
2. Angular Momentum of a System of Particles
3. Total Energy of a System of Particles
4. The Principle of Virtual Displacements, D’Alembert’s Principle and the Lagrangian Equations of the
First Kind
5. The Lagrangian Equations of the Second Kind for Arbitrary Coordinates (Generalized Co-ordinates)
6. Generalized Momentum Co-ordinates. Hamilton’s Equations
7. Hamilton’s Principle
8. Canonical Transformations
9. Cyclic Variables. The Hamilton-Jacobi Differential Equation
10. Periodic and Multiply Periodic Systems. Angle Variables; the Angle Variables of the Keplerian
Motion
CHAPTER VII
The Mechanics of Rigid Bodies
1. Selected Topics in the Kinematics of Rigid Bodies
2. General Statics and Dynamics of Rigid Bodies. Equivalence of Systems of Forces acting upon Rigid
Bodies
3. Rotation of a Rigid Body about a Fixed Axis. Moment of Inertia and its Calculation
4. Motion of a Rigid Body about a Fixed Point. Elements of the Theory of the Top
CHAPTER VIII
Elasticity: The Mechanics of Deformable Solids
1. The Geometry of Small Displacements
2. State of Stress of a Body under Strain
3. The Conditions of Equilibrium of an Elastic Body
4. Relations between the Strain Tensor and the Stress Tensor
5. Energy of Elastically Deformed Bodies; Elastic Potential
6. Elementary Treatment of the Bending of a Cantilever Beam
7. Waves in Unbounded Elastic Media (Seismic Waves.) Longitudinal Waves in Bars
8. Transverse Vibration of Stretched Strings and Membranes
CHAPTER IX
The Mechanics of Liquids and Gases
(Hydro- and Aero-Mechanics)
1. Equilibrium of Fluid Bodies (Hydrostatics)
2. The Fundamental Hydrodynamical Equations