Theoretical Physics [3 ed.]

Table of contents :
Preface To The Second Edition
Preface ToThe Third Edition
Contents
Introduction
Part 1: Mathematical Introduction
Chapter 1: 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 2: 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 3: 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 4: 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 2: Mechanics
Chapter 5: 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 6: 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 7: 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 8: 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 9: The Mechanics of Liquids and Gases (Hydro- and Aero-Mechanics)
1. Equilibrium of Fluid Bodies (Hydrostatics)
2. The Fundamental Hydrodynamical Equations
3. Irrotational Flow
4. General Theorems concerning Vortex and Circulation
5. Plane Circulatory Motion
6. Undulatory Propagation of Disturbances in Fluids (Sound Waves)
7. Hydrodynamics of Viscous Fluids
8. Surface Tension of Liquids
Chapter 10: Relativistic Mechanics
1. Space and Time in Newtonian Mechanics
2. Inertial Frames. The Galilean Transformation
3. Accelerated Frames of Reference. Free Fall on the Rotating Earth
4. Moving Frames of Reference in Acoustics. The Doppler Effect
5. Moving Frames of Reference in Optics. The Michelson-Morley Experiment
6. The Relativistic Conception of Space and Time. The Lorentz Transformation
7. Immediate Consequences of the Lorentz Transformation
8. Geometric Representation of the Lorentz Transformation. The Fourdimensional World. Calculation with World-vectors
9. Newton’s Second Law in the Theory of Relativity. The Variability of Mass and the Inertia of Energy
10. Fundamental Concepts of the Generalized Theory of Relativity
Part 3: Field Theory of Electromagnetic and Optical Phenomena
Chapter 11: The Electrostatic Field in a Vacuum (or in Air)
1. Definitions
2. Electrical Charge (Quantity of Electricity) as the Source of Flux
3. The Electrostatic Potential
4. Simple Examples of the Electrostatic Field in a Vacuum (or in Air)
Chapter 12: The Electrostatic Field in Dielectric Media
1. Formal Introduction of the Concepts “ Dielectric Displacement ” and “ Free Charge ”. Boundary Conditions at the Surface of Separation of Two Dielectrics
2. Polarization of Dielectrics
3. Simple Examples of the Electrostatic Field in Dielectrics
Chapter 13: Energy and Ponderomotive Forces in the Electrostatic Field
1. Potential Energy of Systems of Charges in a given Field
2. Total Energy of the Electrostatic Field.
3. Forces and Equilibrium in the Electrostatic Field. Theory of the Manometer Method for the Electrical Susceptibility of a Liquid
Chapter 14: Stationary Electric Fields and Steady Currents
1. Ohm’s Law
2. Generation of Heat in a steady Electric Field
Chapter 15: The Magnetostatic Field
1. Comparison of Electrostatic and Magnetostatic Fields
2. Calculation of the Magnetostatic Field accompanying a given Distribution of Electric Currents in a Vacuum
3. Calculation of the Magnetic Field accompanying Electric Currents when Ferromagnetic Materials are present
4. Ponderomotive Forces on Conductors in a Magnetic Field
Chapter 16: Slowly Varying (Quasi-stationary) Fields
1. The Law of Induction. Maxwell’s Equations
2. Self and Mutual Induction
3. Steady Alternating-current Circuits
4. Non-stationary States (Transient Phenomena) in Alternating-current Circuits
5. Resistance and Inductance of Wires for Alternating Currents. Skin Effect
Chapter 17: Rapidly Alternating Electromagnetic Fields: I—Propagation in Homogeneous Isotropic Media
1. The Electrical Analogue of the Law of Induction
2. The Wave Equation for the Propagation of Fields in Dielectrics
3. The Poynting Vector of Energy Flow.
4. Propagation of Electromagnetic Waves in Conduction Media
5. Hertz’s Solution of the Field Equations. The Hertzian Oscillator
Chapter 18: Electromagnetic Waves: II–Phenomena in Two Adjoining Media
1. Unified Rigorous Derivation of the Field Equations and of the Boundary Conditions
2. Waves in the Boundary Layer. The Ground Wave
3. Consequence of the Boundary Conditions for Insulating Media. The Optical Laws of Reflection and Refraction
4. Polarization and Intensity Relationships for Reflection and Refraction. Fresnel’s Formulae
5. Total Reflection
6. Absorbing Media. The Optics of Metals
Chapter 19: Electromagnetic Waves: III–Propagation in Anisotropic Media. The Optics of Crystals
1. The Field Equations for Anisotropic Bodies
2. Plane Electromagnetic Waves in Anisotropic Media
3. Normal Surface and Wave Surface. The Optical Axes
4. Refraction of Plane Waves at the Surface of an Anisotropic Medium
Chapter 20: Electromagnetic Waves: IV–The Theory of Diffraction
1. The General Diffraction Problem and Attempts to solve it. Kirchoff’s Formula
2. Reciprocal Theorems of the Theory of Diffraction. Classification of Diffraction Phenomena
3. Fraunhofer Diffraction by a Slit and by One-, Two- and Three-dimensional Gratings
4. Fresnel Diffraction Phenomena at a Slit and at a Circular Aperture. Zone Plates
Chapter 21: The Elements of Geometrical Optics and of Interference Optics
1. The Fundamentals of Geometrical Optics. Laws of Fermat and of Malus
2. The Properties of Collinear Projection
3. The Practical Problem of Image Formation. Abbe’s Sine Law. General Path of an Elementary Pencil from a Point Source
4. The Resolving Power of Optical Systems
5. The Fundamentals of Interference Optics. Interference Fringes
Part 4: The Theory of Electricity. II. The Atomistic Nature of Electrical Phenomena
Chapter 22: Electrolytic Conduction
1. The Fundamental Phenomena of Electrolytic Conduction and their Interpretation
2. Dependence of Electrolytic Conductivity upon Concentration. The Theory of Debye-Hückel and Onsager
Chapter 23: The Conduction of Electricity in Gases
1. Direct Determination of the Elementary Electrical Charge by the Millikan Oil Drop Method
2. The Nature of the Cathode Ray Particles. The Electron
3. Survey of the Possible Methods of Generating Carriers of Electricity in Gases
4. The Separately-sustained Electrical Discharge. Spark Discharge
5. Self-maintaining Discharge; Glow and Arc Discharge
6. The Origin of Cathode, Canal, and Positive Rays. The Mass Spectrograph
Chapter 24: The Fundamental Ideas of the Theory of Metallic Conduction
1. Electrons as Carriers of Current in Metals
2. Derivation of Ohm’s Law for Metals
3. Conduction of Heat in Metals; the Law of Wiedemann and Franz
4. Objections to the Theory developed above. The Electron Theory of Pauli and Sommerfeld
Chapter 25: Electron Theory of the Dielectric Constant, Index of Refraction and Magnetic Permeability
1. The Origin of Electrical and Magnetic Polarization
2. Theory of Dielectric Polarization, Optical Index of Refraction and Dispersion
3. Parelectric Susceptibility
4. Paramagnetic, Ferromagnetic and Antiferromagnetic Susceptibility
5. Magnetism Induced by Revolving Electrons. The Magnetomechanical Parallelism. Theory of Diamagnetic Susceptibility
Chapter 26: Phenomenological Theory of Superconductivity
1. The Fundamental Equations
2. Steady Fields
3. Optical Behaviour of Superconductors
Chapter 27: The Electrodynamics of Moving Bodies
1. Electromagnetic Induction in Moving Bodies from the Standpoint of the Electron Theory
2. Magnetic Effects of Moving Charges
3. Propagation of Electromagnetic Waves in Moving Media
4. Relativistic-invariant Form of the Electromagnetic Equations
Part 5: The Theory of Heat. Phenomenological Part
Chapter 28: Theory of the Conduction of Heat
1. Definition of Temperature, Quantity of Heat, Thermal Capacity and Specific Heat
2. The Differential Equation of Heat Conduction; Initial and Boundary Conditions
3. A Simple Example of the Integration of the Equation of Heat Conduction: Penetration of the Daily and Yearly Temperature Variations into the Interior of the Earth
Chapter 29: The Equation of State of Thermodynamic Systems
1. Definition of the Thermodynamic Variables and the Relationships between them
2. The Equation of State of an Ideal Gas
3. The Equation of State of a Real Gas
Chapter 30: The First Law of Thermodynamics: The Conservation of Energy
1. Formulation of the First Law
2. Specific Heat at Constant Volume and at Constant Pressure. The Energy Function of a Gas
3. Adiabatic Change
4. Application of the First Law to Thermochemistry
Chapter 31: The Second Law of Thermodynamics: The Law of Entropy
1. The Carnot Cycle and the Ideal Heat Engine
2. Formulation and Interpretation of the Second Law
3. Conditions of Equilibrium for Systems under Various Conditions. Thermodynamic Potentials
4. Connexion between the Internal Energy and the Equation of State
5. Electrocaloric and Magnetocaloric Phenomena
Chapter 32: Application of the Second Law to the Calculation of the Equilibrium of Thermodynamic Systems
1. Gibbs' Phase Rule: a General Theorem on the Maximum Number of Possible Phases
2. The Vapour Pressure Curve and the Melting-point Curve
3. Chemical Equilibrium in a Mixture of Ideal Gases. The Law of Mass Action
4. Chemical Equilibrium in a System consisting of Dilute Solutions and Ideal Gases
5. Thermodynamic Equilibrium of Dilute Solutions of Strong Electrolytes
Chapter 33: The Nernst Heat Theorem
1. Free Energy as a Measure of Chemical Affinity; Determination of this Quantity for the Galvanic Cell
2. Formulation of the Nernst Heat Theorem
3. Consequences for the Specific Heats and Temperature Coefficients. The Chemical Constant of a Gas
4. Unattainability of the Absolute Zero
Part 6: The Theory of Heat. Statistical Part
Chapter 34: The Elementary Kinetic Theory of Matter
1. Bernoulli’s Formula; Boyle’s Law
2. Number of Collisions and Mean Free Path for Real Gases
3. Viscosity and Heat Conduction in Gases. Determination of Avogadro’s Number and of the Size of the Molecule
4. Derivation of some Properties of Crystals on the Molecular Theory
Chapter 35: The Classical Statistics of Boltzmann
1. Entropy and Probability
2. Calculation of the most Probable Distribution of Density in an Ideal Gas
3. Representation of the Distribution of Position and Velocity by means of Phase Space. Liouville’s Theorem
4. The Maxwell-Boltzmann Energy Distribution
5. Applications of the Maxwell-Boltzmann Energy Distribution
6. The Law of Equipartition and its Application to the Specific Heats
7. Fluctuations. Transition from Microscopic to Macroscopic Motion
Chapter 36: The Classical Quantum Statistics
1. The Quantum Condition for the Subdivision of the Phase Space of an Oscillator
2. Temperature Variation of the Vibrational Contribution to the Specific Heats
3. The Debye Theory of the Specific Heats of Solids
Chapter 37: The Theory of Thermal Radiation
1. Analogy between a Gas and Radiation filling an Enclosure. Radiation Pressure
2. The Connexion between Energy Density and Surface Brightness
3. The Connexion between Emission and Absorption in Thermodynamic Equilibrium. Kirchhoff’s Law
4. Planck’s Law of Radiation
Chapter 38: The Bose-Einstein and the Fermi-Dirac Statistics
1. Preliminary Remarks concerning the Duality of Waves and Corpuscles
2. The Bose-Einstein Statistics
3. The Fermi-Dirac Statistics and its Application to Electrical Conductivity
4. Entropy Constant and Chemical Constant of an Ideal Monatomic Gas
Part 7: The Structure of Atoms and Molecules And the Theory of Spectra
Chapter 39: The Mechanics of Simple Atomic Models
1. Investigation of the Structure of the Atom; the Scattering of x
2. Conclusions from the Experiments on the Scattering of α-Particles
3. The Bohr Model of the Hydrogen Atom
4. Consideration of the Motion of the Nucleus. The Spectrum of Hydrogen and the Spectrum of Ionized Helium
5. X-ray Spectra. Moseley’s Law
6. The Correspondence Principle
7. The Atomic Spectra of the Alkalis, the Alkaline Earths and Similar Systems
8. Perturbation of Electron Orbits by External Forces. Stark Effect and Zeeman Effect
9. Difficulties arising in the Atomic Theory of Magnetism. Explanation in Terms of the Spinning Electron
10. The Theory of Multiplets and of their Zeeman Effects. Quantum Theory of Paramagnetic Susceptibility
11. The Structure of the Periodic System of the Elements. Pauli’s Principle
12. Elements of the Theory of Band Spectra
Chapter 40: Critical Atomic Theory: The New Quantum Mechanics
1. The Wave and Particle Aspects of Light. Compton Effect and Raman Effect
2. The Inexactness of Atomic Observations
3. Matter Waves
4. The Proper Values of the Wave Equation
5. The Hydrogen Atom
6. Rotation Spectra of Diatomic Molecules
7. The Physical Meaning of the Ψ Function. Intensity Relations for Spectral Lines
Chapter 41: Atomic Problems First Solved by the Wave Mechanics
1. The Theory of Perturbations in Wave Mechanics
2. The Chemical Bond. Formation of the Hydrogen Molecule
3. The Theory of Dispersion and of the Raman Effect in Wave Mechanics
4. The Surmounting of Potential Barriers in the Wave Mechanics
5. Energy Bands of Electrons in Metals
6. The Role of Lattice Defects in Dielectric Crystals
Chapter 42: Nuclear Physics
1. General Remarks on the Physics of the Atomic Nucleus
2. The Hyperfine Structure of Spectral Lines as a Connecting Link between the Physics of the Outer Shells and that of the Nucleus
3. Radioactivity
4. Artificial Transformation and Excitation of the Nucleus
5. The Neutron
6. The Positron
7. Artificial Radioactivity
8. The Role of Protons and Neutrons in Nuclear Structure
9. The Liquid Drop Model of the Nucleus
10. The Fission of Uranium
11. Liquid Drop Treated as a Fermi Gas
12. Independent Particle and Shell Models of the Nucleus; Nuclear Moments
13. Beta Transformations and the Neutrino Hypothesis
14. Mesons
15. Brief Survey of our Knowledge concerning Cosmic Rays
Part 8: Selected Topics From Several Fields of Technical Importance
Chapter 43: Further Matters Connected with the Geometric Optics of Light and of Electrons
1. Condition for Absence of Distortion and its Relation to the Sine Condition
2. Focal Length of an Electron Lens
Chapter 44: Piezoelectricity and its Applications
1. The Phenomenon of Piezoelectricity
2. Application of Piezoelectricity to the Stabilization of Oscillating Circuits
Chapter 45: Space-charge Effects in Gaseous Discharges
1. Characteristic Curve of a Thermionic Tube
2. Oscillations of a Plasma
Chapter 46: Theory of Elastomers
1. Behaviour of High-polymer Chain Molecules
2. A Model of Muscular Action
Mathematical Addendum
1. Generalization of x
2. Bessel Functions of the First Kind
3. Bessel Functions of the Second and Third Kinds. Asymptotic Values of Bessel Functions
4. Spherical Harmonics
Solutions of The Exercises
Tables
References for Further Study
Index