The Unity of Science

Cover\nHalf Title\nTitle Page\nCopyright Page\nDedication\nContents\nPreface\nAcknowledgements\nChapter 1: The Unity of Science\n	1.1. Introduction\n	1.2. The Invention of Mathematics\nChapter 2: Classical Mechanics\n	2.1. ♦ Newton’s Laws of Motion\n	2.2. ♦ Newton’s Law of Gravitation\n		2.2.1. Gravitational Potential and Energy Conservation\nChapter 3: Electromagnetism\n	3.1. ♦ Electrostatics\n		3.1.1. ♦ Coulomb’s Law\n		3.1.2. Applications of Coulomb’s Law\n			3.1.2.1. Lightning\n			3.1.2.2. The Field of a Dipole\n			3.1.2.3. Piezo-Electricity\n		3.1.3. ♦ Gauss’s Theorem\n		3.1.4. Applications of Gauss’s theorem\n			3.1.4.1. The Capacitor\n			3.1.4.2. Measuring the Charge of the Electron\n			3.1.4.3. The Electrostatic Lens\n		3.1.5. Solving Poisson’s Equation\n			3.1.5.1. The Method of Images\n		3.1.6. Electric Field in Matter: Dielectrics\n	3.2. ♦ Magnetostatics\n		3.2.1. ♦ Volta’s Battery and Ohm’s Law\n		3.2.2. ♦ Electrostatics, Magnetostatics and Relativity: the Lorentz Force\n		3.2.3. Applications of the Lorentz Force\n			3.2.3.1. Aurora Borealis\n			3.2.3.2. The Particle Accelerator\n			3.2.3.3. The Penning trap\n		3.2.4. ♦ Ampère’s Law\n		3.2.5. Applications of Ampère’s Law\n			3.2.5.1. Magnetic Field of a Current Segment\n			3.2.5.2. Magnetic Field of a Current Loop\n			3.2.5.3. The Solenoid\n			3.2.5.4. D’Arsonval’s Galvanometer\n		3.2.6. Magnetic Fields in Matter: Permeability and Permanent Magnets\n	3.3. ♦ Electromagnetic Induction\n		3.3.1. ♦ Faraday’s Law\n		3.3.2. Applications of Faraday’s Law\n			3.3.2.1. Inductance\n			3.3.2.2. The Electric Transformer\n			3.3.2.3. Electric Motor and Alternating Current (AC) Generator\n			3.3.2.4. Electronic Circuits\n	3.4. ♦ Maxwell’s Equations\n		3.4.1. ♦ Energy Conservation and Radiated Power\n		3.4.2. Applications of Maxwell’s Equations\n			3.4.2.1. The Radiating Dipole\n			3.4.2.2. The Dipole Antenna\n			3.4.2.3. The Paradox of Atomic Stability\n			3.4.2.4. The Color of the Sky\n			3.4.2.5. The Doppler-Fizeau Effect and the Expansion of the Universe\n			3.4.2.6. The Darkness of Night\n	3.5. Optics\n		3.5.1. Electromagnetic Waves in Matter: Refraction\n		3.5.2. Fermat’s Principle\n			3.5.2.1. Geometrical Optics\n		3.5.3. Diffraction\n		3.5.4. Dispersion of Light and the Colors of the Rainbow\nChapter 4: Quantum Mechanics\n	4.1. ♦ The Puzzles of Matter and Radiation\n		4.1.1. ♦ Black-Body Radiation\n			4.1.1.1. The Sun and Earth Temperatures\n			4.1.1.2. The Universe as a Perfect Black-Body\n		4.1.2. The Photo-Electric Eect\n			4.1.2.1. Digital Cameras and Solar Cells\n		4.1.3. Bohr’s Atom and the Spectrum of Hydrogen\n			4.1.3.1. Particle-Wave Duality\n			4.1.3.2. The Bohr-Sommerfeld Quantization Rule\n		4.1.4. Absorption and Stimulated Emission\n	4.2. ♦ Quantum Mechanical Formalism\n		4.2.1. ♦ Example: Particle in a Box\n	4.3. Simple QM systems\n		4.3.1. The Chiral Ammonia Molecule\n			4.3.1.1. Schrödinger’s Cat\n			4.3.1.2. Bell’s Inequalities\n		4.3.2. The Ammonia Molecule in an Electric Field\n			4.3.2.1. The Ammonia Maser\n		4.3.3. The Energy Spectrum of Aromatic Molecules\n		4.3.4. Conduction Bands in Solids\n	4.4. ♦ Momentum, Space and Energy Operators\n		4.4.1. ♦ Heisenberg Uncertainty Principle\n	4.5. ♦ Schrödinger’s Equation\n		4.5.1. Particle-Wave Duality: Diraction\n		4.5.2. Particle Interference Observed with Buckyballs\n		4.5.3. Particle-Wave Duality: Refraction\n		4.5.4. The Scanning Tunneling Microscope\n		4.5.5. ♦ The Correspondence Principle\n	4.6. ♦ Dirac’s Equation: Antiparticles and Spin\n		4.6.1. Spin and Magnetic Dipole\n		4.6.2. Antiparticles\n	4.7. Angular Momentum Wavefunction\n	4.8. ♦ The Hydrogen Atom and Electronic Orbitals\n	4.9. ♦ Many Electron Systems\n		4.9.1. ♦ The Periodic Table of the Elements\n	4.10. The Chemical Bond\n		4.10.1. Variational Approach to Molecular Energy Levels\n			4.10.1.1. Hückel’s Molecular Orbital Theory\n		4.10.2. Molecular Rotational Spectrum\n		4.10.3. Molecular Vibrational Spectrum\n	4.11. Time Independent Perturbation Theory\n		4.11.1. Energy Levels in Non-Hydrogen Atoms\n		4.11.2. The Stark Eect\n			4.11.2.1. Quantum Wells\n			4.11.2.2. Diatomic Molecules\n		4.11.3. The Zeeman Eect\n			4.11.3.1. Magnetic Resonance Imaging (MRI)\n	4.12. Time Dependent Perturbation Theory\n		4.12.1. Transitions between Electronic Energy Levels\n		4.12.2. Molecular Rotational-Vibrational Transitions\n		4.12.3. Absorption and Fluorescence Emission\n			4.12.3.1. Super-Resolution Microscopy\n			4.12.3.2. The Laser\nChapter 5: Statistical Mechanics\n	5.1. ♦ Probability Theory\n		5.1.1. ♦ Random Walk\n		5.1.2. Diffusion\n		5.1.3. Central Limit Theorem\n	5.2. ♦ Missing Information, Guessing and Entropy\n		5.2.1. Information, Shannon Entropy and Coding\n		5.2.2. ♦ Guessing the Odds for Fair and Loaded Die\n	5.3. Paramagnetism\n		5.3.1. Paramagnetism and the Ising model\n		5.3.2. Paramagnetism from Enumeration of States\n		5.3.3. Second Law of Thermodynamics\n	5.4. The Freely Jointed Chain Model of a Polymer\n	5.5. ♦ Ideal Gas\n		5.5.1. Kinetic Theory of Gases\n		5.5.2. Temperature Equilibration, Specific heats\n		5.5.3. Heat and Work\n	5.6. Equipartition Theorem\n	5.7. Variable Number of Particles\n		5.7.1. Boiling Pressure and Latent Heat of Vaporization\n		5.7.2. The Voltage Across a Cell Membrane\n		5.7.3. Chemical Reactions\n		5.7.4. Adsorption\n	5.8. Comparison of Thermodynamic Relations for Non-Interacting Systems\n	5.9. Quantum Statistics\n		5.9.1. Planck’s Black-body Radiation\n		5.9.2. ♦ Fermi-Dirac Statistics\n			5.9.2.1. White Dwarfs and Black Holes\n			5.9.2.2. ♦ Conductors and Semiconductors\n			5.9.2.3. ♦ Diodes and Photodiodes\n			5.9.2.4. ♦ The Field Effect Transistor\n		5.9.3. Bose-Einstein Statistics\n			5.9.3.1. Superconductors and Superfluids\n	5.10. Interacting Systems\n		5.10.1. Ferromagnetism\n		5.10.2. Real Gases\n			5.10.2.1. The Joule Effect and Refrigeration\n		5.10.3. DNA as a Model Polymer\n	5.11. Out of Equilibrium Systems\n		5.11.1. Near Equilibrium Transport Properties\n			5.11.1.1. Diffusion\n			5.11.1.2. Heat Conduction\n			5.11.1.3. Viscosity\n		5.11.2. Hydrodynamics: the Navier-Stokes Equations\n		5.11.3. Dissipation-Fluctuation Theorem\n	5.12. Biology\nAppendix A: Appendix\n	A.1. Some Physical Constants\n	A.2. Linear Algebra\n		A.2.1. Eigenvalues and Eigenvectors\n	A.3. Vector Calculus\n		A.3.1. Taylor Expansions\n	A.4. Fourier Transforms\n		A.4.1. Properties of the Fourier Transform\n	A.5. Laplace and Helmholtz Equations\n		A.5.1. Solutions for a Rectangular Geometry\n		A.5.2. Solutions for a Cylindrical Geometry\n		A.5.3. Solutions for a Spherical Geometry\n			A.5.3.1. Solutions of the Angular Equation\n			A.5.3.2. Solutions of the Radial Equation\n	A.6. ♦ Special Relativity\n		A.6.1. Lorentz Invariance and Relativity\n	A.7. Advanced Topics in Electromagnetism\n		A.7.1. Solution of Laplace Equation in Two Dimensions\n		A.7.2. Physical Optics\n			A.7.2.1. The Resolution Limit\n			A.7.2.2. Optical Image Processing\n	A.8. Advanced Topics in Quantum Mechanics\n		A.8.1. Quantum Tunneling\n		A.8.2. Gauge Invariance: the Aharonov-Bohm Effect\n		A.8.3. Angular Momentum Representation\n			A.8.3.1. Total Angular Momentum Eigenstates\n		A.8.4. Perturbation Theory with Degenerate Eigenstates\n			A.8.4.1. The Stark Effect in Hydrogen\n	A.9. Advanced Topics in Statistical Mechanics\n		A.9.1. Specific Heat of Solids\n		A.9.2. The Bipolar Transistor\n		A.9.3. Critical Phenomena\n			A.9.3.1. The Ising Model Near its Critical Temperature: Critical Exponents\n			A.9.3.2. Real Gas Near its Critical Point\n		A.9.4. Monte-Carlo Methods\nReferences\nIndex