Stauffer / Stanley From Newton to Mandelbrot

A Primer in Theoretical Physics
1990
ISBN: 978-3-642-97262-1
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 191 Seiten, eBook

From Newton to Mandelbrot takes the student on a tour of the most important landmarks of theoretical physics: classical, quantum, and statistical mechanics, relativity, electrodynamics, and, the most modern and exciting of all, the physics of fractals. The treatment is confined to the essentials of each area, and short computer programs, numerous problems, and beautiful colour illustrations round off this unusual textbook. Ideally suited for a one-year course in theoretical physics it will prove indispensable in preparing and revising for exams.

Zielgruppe

Research

Autoren/Hrsg.

Stauffer, Dietrich

Stanley, H. Eugene

Weitere Mitwirkende

Armstrong, A.H.

Inhaltsverzeichnis

1. Mechanics.- 1.1 Point Mechanics.- 1.1.1 Basic Concepts of Mechanics and Kinematics.- 1.1.2 Newton’s Law of Motion.- 1.1.3 Simple Applications of Newton’s Law.- 1.1.4 Harmonic Oscillator in One Dimension.- 1.2 Mechanics of Point Mass Systems.- 1.2.1 The Ten Laws of Conservation.- 1.2.2 The Two-body Problem.- 1.2.3 Constraining Forces and d’Alembert’s Principle.- 1.3 Analytical Mechanics.- 1.3.1 The Lagrange function.- 1.3.2 The Hamilton function.- 1.3.3 Harmonic Approximation for Small Oscillations.- 1.4 Mechanics of Rigid Bodies.- 1.4.1 Kinematics and Inertia Tensor.- 1.4.2 Equations of Motion.- 1.5 Continuum Mechanics.- 1.5.1 Basic Concepts.- 1.5.2 Stress, Strain and Hooke’s Law.- 1.5.3 Waves in Isotropic Continua.- 1.5.4 Hydrodynamics.- 2. Electricity and Magnetism.- 2.1 Vacuum Electrodynamics.- 2.1.1 Steady Electric and Magnetic Fields.- 2.1.2 Maxwell’s Equations and Vector Potential.- 2.1.3 Energy Density of the Field.- 2.1.4 Electromagnetic Waves.- 2.1.5 Fourier Transformation.- 2.1.6 Inhomogeneous Wave Equation.- 2.1.7 Applications.- 2.2 Electrodynamics in Matter.- 2.2.1 Maxwell’s Equations in Matter.- 2.2.2 Properties of Matter.- 2.2.3 Wave Equation in Matter.- 2.2.4 Electrostatics at Surfaces.- 2.3 Theory of Relativity.- 2.3.1 Lorentz Transformation.- 2.3.2 Relativistic Electrodynamics.- 2.3.3 Energy, Mass and Momentum.- 3. Quantum Mechanics.- 3.1 Basic Concepts.- 3.1.1 Introduction.- 3.1.2 Mathematical Foundations.- 3.1.3 Basic Axioms of Quantum Theory.- 3.1.4 Operators.- 3.1.5 Heisenberg’s Uncertainty Principle.- 3.2 Schrödinger’s Equation.- 3.2.1 The Basic Equation.- 3.2.2 Penetration.- 3.2.3 Tunnel Effect.- 3.2.4 Quasi-classical WKB Approximation.- 3.2.5 Free and Bound States in the Potential Well.- 3.2.6 Harmonic Oscillators.- 3.3 Angular Momentum and the Structure of the Atom.- 3.3.1 Angular Momentum Operator.- 3.3.2 Eigenfunctions of L2 and Lz.- 3.3.3 Hydrogen Atom.- 3.3.4 Atomic Structure and the Periodic System.- 3.3.5 Indistinguishability.- 3.3.6 Exchange Reactions and Homopolar Binding.- 3.4 Perturbation Theory and Scattering.- 3.4.1 Steady Perturbation Theory.- 3.4.2 Unsteady Perturbation Theory.- 3.4.3 Scattering and Born’s First Approximation.- 4. Statistical Physics.- 4.1 Probability and Entropy.- 4.1.1 Canonical Distribution.- 4.1.2 Entropy, Axioms and Free Energy.- 4.2 Thermodynamics of the Equilibrium.- 4.2.1 Energy and Other Thermodynamic Potentials.- 4.2.2 Thermodynamic Relations.- 4.2.3 Alternatives to the Canonical Probability Distribution.- 4.2.4 Efficiency and the Carnot Cycle.- 4.2.5 Phase Equilibrium and the Clausius-Clapeyron Equation.- 4.2.6 Mass Action Law for Gases.- 4.2.7 The Laws of Henry, Raoult and van’t Hoff.- 4.2.8 Joule-Thomson Effect.- 4.3 Statistical Mechanics of Ideal and Real Systems.- 4.3.1 Fermi and Bose Distributions.- 4.3.2 Classical Limiting Case ?? ? ??.- 4.3.3 Classical Equidistribution Law.- 4.3.4 Ideal Fermi-gas at Low Temperatures ?? ? +?.- 4.3.5 Ideal Bose-gas at Low Temperatures ?? ? 0.- 4.3.6 Vibrations.- 4.3.7 Virial Expansion for Real Gases.- 4.3.8 Van der Waals’ Equation.- 4.3.9 Magnetism of Localised Spins.- 4.3.10 Scaling Theory.- 5. Fractals in Theoretical Physics.- 5.1 Non-random Fractals.- 5.2 Random Fractals: The Unbiased Random Walk.- 5.3 ‘A Single Length’.- 5.3.1 The Concept of a Characteristic Length.- 5.3.2 Higher Dimensions.- 5.3.3 Additional Lengths that Scale with ?t.- 5.4 Functional Equations and Scaling: One Variable.- 5.5 Fractal Dimension of the Unbiased Random Walk.- 5.6 Universality Classes and Active Parameters.- 5.6.1 Biased Random Walk.- 5.6.2 Scaling of the Characteristic Length.- 5.7 Functional Equations and Scaling: Two Variables.- 5.8 Fractals and the Critical Dimension.- 5.9 Fractal Aggregates.- 5.10 Fractals in Nature.- Appendix: Exercises.- A.1 Mechanics, Electricity and Magnetism.- A.2 Quantum Mechanics and Statistical Physics.- Further Reading.- Name and Subject Index.