Foundations of Modern Physics

In addition to his ground-breaking research, Nobel Laureate Steven Weinberg is known for a series of highly praised texts on various aspects of physics, combining exceptional physical insight with a gift for clear exposition. Describing the foundations of modern physics in their historical context and with some new derivations, Weinberg introduces topics ranging from early applications of atomic theory through thermodynamics, statistical mechanics, transport theory, special relativity, quantum mechanics, nuclear physics, and quantum field theory. This volume provides the basis for advanced undergraduate and graduate physics courses as well as being a handy introduction to aspects of modern physics for working scientists. Steven Weinberg is a member of the Physics and Astronomy Departments at the University of Texas at Austin. He has been honored with numerous awards, including the Nobel Prize in Physics, the National Medal of Science, the Heinemann Prize in Mathematical Physics, and most recently a Special Breakthrough Prize in Fundamental Physics. He is a member of the US National Academy of Sciences, the UK’s Royal Society, and other academies in the US and internationally. The American Philosophical Society awarded him the Benjamin Franklin medal, with a citation that said he is “considered by many to be the preeminent theoretical physicist alive in the world today.” He has written several highly regarded books, including Gravitation and Cosmology, the three-volume work The Quantum Theory of Fields, Cosmology, Lectures on Quantum Mechanics, and Lectures on Astrophysics. Foundations of Modern Physics Contents Preface 1 Early Atomic Theory 1.1 Gas Properties Experimental Relations Temperature Scales Theoretical Explanations 1.2 Chemistry Elements Law of Combining Weights Law of Combining Volumes The Gas Constant Avogadro’s Number 1.3 Electrolysis Early Electricity Early Magnetism Electromagnetism Discovery of Electrolysis 1.4 The Electron 2 Thermodynamics and Kinetic Theory 2.1 Heat and Energy Heat as Energy Kinetic Energy Specific Heat Adiabatic Changes 2.2 Absolute Temperature 2.3 Entropy Neutral Matter The Laws of Thermodynamics 2.4 Kinetic Theory and Statistical Mechanics The Maxwell–Boltzmann Distribution The General H-Theorem Canonical and Grand Canonical Ensembles Connection with Thermodynamics Compound Systems Gases Equipartition Entropy as Disorder 2.5 Transport Phenomena Conservation Laws Momentum Flow Galilean Relativity Navier–Stokes Equation Viscosity Mean Free Path Diffusion 2.6 The Atomic Scale Nineteenth Century Estimates Electronic Charge Brownian Motion Black Body Radiation Consistency Appendix: Einstein’s Diffusion Constant Rederived 3 Early Quantum Theory 3.1 Black Body Radiation Radiation Absorption, Emission, and Energy Density Electromagnetic Degrees of Freedom The Rayleigh–Jeans Distribution The Planck Distribution Finding the Boltzmann Constant Radiation Energy Constant 3.2 Photons Quantization of Radiation Energy Derivation of Planck Distribution Photoelectric Effect Particles of Light 3.3 The Nuclear Atom Radioactivity Discovery of the Atomic Nucleus Nuclear Mass Nuclear Size Scattering Pattern Nuclear Charge 3.4 Atomic Energy Levels Spectral Lines Electron Orbits The Combination Principle Bohr’s Quantization Condition The Correspondence Principle Comparison with Observed Spectra Reduced Mass Atomic Number Outstanding Questions 3.5 Emission and Absorption of Radiation A and B Coefficients Lasers Suppressed Absorption 4 Relativity 4.1 Early Relativity Motion of the Earth Relativity of Motion Speed of Light Michelson–Morley Experiment 4.2 Einsteinian Relativity Postulate of Invariance Lorentz Transformations The Galilean Limit Maximum Speed General Directions Special and General Relativity 4.3 Clocks, Rulers, Light Waves Clocks Rulers Light Waves 4.4 Mass, Energy, Momentum, Force Einstein’s Thought Experiment General Formulas for Energy and Momentum E = mc^2 Force 4.5 Photons as Particles Photon Momentum Compton Scattering 4.6 Electromagnetic Fields and Forces Density and Current The Inhomogeneous Maxwell Equations Upstairs, Downstairs The Homogeneous Maxwell Equations Electric and Magnetic Forces 4.7 Causality Invariance of Temporal Order Light Cone 5 Quantum Mechanics 5.1 De Broglie Waves Application to Hydrogen Group Velocity Davisson–Germer Experiment Appendix: Derivation of the Bragg Formula 5.2 The Schrödinger Equation Wave Equation in a Potential Boundary Conditions Spherical Symmetry Radial and Angular Wave Functions Angular Multiplicity Spherical Harmonics Hydrogenic Energy Levels 5.3 General Principles of Quantum Mechanics States and Wave Functions Observables and Operators The Hamiltonian Adjoints Expectation Values Probabilities Continuum Limit Momentum Space Commutation Relations Uncertainty Principle Time Dependence Conservation Laws Heisenberg and Schrödinger Pictures 5.4 Spin and Orbital Angular Momentum Spin Discovered Rotations Spin and Orbital Angular Momenta Multiplets Adding Angular Momenta Fine Structure and Space Inversion Hyperfine Structure Appendix: Clebsch–Gordan Coefficients 5.5 Bosons and Fermions Identical Particles Statistics The Hartree Approximation The Pauli Exclusion Principle The Periodic Table Diatomic Molecules 5.6 Scattering Scattering Wave Function Representations of the Delta Function Calculation of the Green’s Function The Scattering Amplitude Probabilistic Interpretation The Born Approximation Coulomb Scattering Appendix: General Transition Rates 5.7 Canonical Formalism Hamiltonian Formalism Lagrangian Formalism Noether’s Theorem 5.8 Charged Particles in Electromagnetic Fields Scalar and Vector Potentials Gauge Transformations Magnetic Interactions Spin Coupling 5.9 Perturbation Theory First-Order Perturbation Theory Zeeman Effect Second-Order Perturbation Theory 5.10 Beyond Wave Mechanics 6 Nuclear Physics 6.1 Protons and Neutrons Discovery of the Proton Electrons in the Nucleus? Discovery of the Neutron Nuclear Radius and Binding Energy Liquid Drop Model Surface Tension Coulomb Repulsion Neutron–Proton Inequality Stable Valley and Decay Modes 6.2 Isotopic Spin Symmetry Nuclear Forces Isotopic Spin Rotations Multiplets Why Isotopic Spin Symmetry? Pions Appendix: The Three–Three Resonance 6.3 Shell Structure 6.4 Alpha Decay Appendix: Quantum Theory of Barrier Penetration Rates 6.5 Beta Decay 7 Quantum Field Theory 7.1 Canonical Formalism for Fields Field Equations Commutation Relations Energy and Momentum 7.2 Free Real Scalar Field 7.3 Interactions Time-Ordered Perturbation Theory Lorentz Invariance Example: Scattering Calculation of the Propagator 7.4 Antiparticles, Spin, Statistics Appendix: Dirac Fields 7.5 Quantum Theory of Electromagnetism Lagrangian Density Gauge Transformations Coulomb Gauge Free Fields Radiative Decay Selection Rules Gauge Invariance and Charge Conservation Local Phase and Matrix Transformations Assorted Problems Bibliography Author Index Subject Index "In addition to his ground-breaking research, Nobel Laureate Steven Weinberg is known for a series of highly praised texts on various aspects of physics, combining exceptional physical insight with a a gift for clear exposition. Describing the foundations of modern physics in their historical context and with some new derivations, Weinberg introduces topics ranging from early applications of atomic theory through thermodynamics, statistical mechanics, transport theory, special relativity, quantum mechanics, nuclear physics, and quantum field theory. This volume provides the basis for advanced undergraduate and graduate physics courses as well as being a handy introduction to aspects of modern physics for working scientists"-- Provided by publisher In addition to his ground-breaking research, Nobel Laureate Steven Weinberg is known for a series of highly praised texts on various aspects of physics, combining exceptional physical insight with his gift for clear exposition. Describing the foundations of modern physics in their historical context and with some new derivations, Weinberg introduces topics ranging from early applications of atomic theory through thermodynamics, statistical mechanics, transport theory, special relativity, quantum mechanics, nuclear physics, and quantum field theory. This volume provides the basis for advanced undergraduate and graduate physics courses as well as being a handy introduction to aspects of modern physics for working scientists. Exploring modern physics in its historical context, topics range from early applications of atomic theory through thermodynamics, statistical mechanics, transport theory, special relativity, quantum mechanics, nuclear physics, and quantum field theory. Advanced undergraduates and working scientists seeking contextualized introductions will benefit.