AN OUTLINE OF PHYSICS
1 Electrostatics I 1 11 Review of F = ma 1 12 Enter electricity 3 13 Coulomb’s law 8 14 Properties of charge 10 141 Superposition principle 12 15 Verifying Coulomb’s law 13 16 The ratio of gravitational to electric forces 15 17 Coulomb’s law for continuous charge density 17 2 The Electric Field 19 21 Review of key ideas 19 22 Digression on nuclear forces 20 23 The electric field E 22 24 Visualizing the field 25 25 Field of a dipole 33 251 Far field of dipole: general case 36 26 Response to a field 38 261 Dipole in a uniform field 39 3 Gauss’s Law I 42 31 Field of an infinite line charge 43 32 Field of an infinite sheet of charge 47 33 Spherical charge distribution: Gauss’s law 52 34 Digression on the area vector dA 53 341 Composition of areas 55 342 An application of the area vector 57 35 Gauss’s law through pictures 59 351 Continuous charge density 64 4 Gauss’s Law II: Applications 65 41 Applications of Gauss’s law 66 42 Field inside a shell 69 43 Field of an infinite charged wire, redux 72 44 Field of an infinite plane, redux 74 45 Conductors 75 451 Field inside a perfect conductor is zero 76 452 The net charge on a conductor will reside at the surface 77 453 A conductor with a hole inside 78 454 Field on the surface of a conductor 79 5 The Coulomb Potential 81 51 Conservative forces and potential energy 82 52 Is the electrostatic field conservative? 88 53 Path independence through pictures 92 54 Potential and field of a dipole 93 6 Conductors and Capacitors 97 61 Cases where computing V from E is easier 99 62 Visualizing V 101 63 Equipotentials 103 64 Method of images 104 641 Proof of uniqueness (optional section) 110 642 Additional properties of the potential V(r) 112 65 Capacitors 113 66 Energy stored in a capacitor 115 67 Energy of a charge distribution 116 7 Circuits and Currents 119 71 Energy in the electric field 120 72 Circuits and conductivity 121 73 Circuits 126 74 The battery and the emf E 130 75 The RC circuit with a battery 135 76 Miscellaneous circuits 138 8 Magnetism I 142 81 Experiments pointing to magnetism 142 82 Examples of the Lorentz force, the cyclotron 147 83 Lorentz force on current-carrying wires 151 84 The magnetic dipole 154 85 The DC motor 156 9 Magnetism II: Biot-Savart Law 158 91 Practice with Biot-Savart: field of a loop 160 92 Microscopic description of a bar magnet 162 93 Magnetic field of an infinite wire 164 94 Amp`ere’s law 167 95 Maxwell’s equations (static case) 172 10 Amp`ere II, Faraday, and Lenz 174 101 Field of an infinite wire, redux 175 102 Field of a solenoid 179 103 Faraday and Lenz 184 104 Optional digression on Faraday’s law 195 11 More Faraday 200 111 Betatron 200 112 Generators 205 113 Inductance 208 114 Mutual inductance 211 115 Self-inductance 214 116 Energy in the magnetic field 217 12 AC Circuits 220 121 Review of inductors 220 122 The LC circuit 226 1221 Driven LC circuit 229 123 The LCR circuit 231 1231 Review of complex numbers 231 1232 Solving the LCR equation 236 1233 Visualizing Z 239 124 Complex form of Ohm’s law 241 13 LCR Circuits and Displacement Current 244 131 Analysis of LCR results 246 1311 Transients and the complementary solution 251 132 Power of the complex numbers 253 133 Displacement current 259 14 ElectromagneticWaves 263 141 The wave equation 266 142 Restricted Maxwell equations in vacuum 270 1421 Maxwell equations involving infinitesimal cubes 270 1422 Maxwell equations involving infinitesimal loops 272 143 The wave! 275 144 Sinusoidal solution to the wave equation 277 145 Energy in the electromagnetic wave 283 146 Origin of electromagnetic waves 285 147 Maxwell equations—the general case (optional) 286 1471 Maxwell equations involving infinitesimal cubes 286 1472 Maxwell equations involving infinitesimal loops 288 1473 Consequences for the restricted E and B 293 148 From microscopic to macroscopic (optional) 294 1481 Maxwell equations involving cubes 295 1482 Maxwell equations involving loops 297 15 Electromagnetism and Relativity 300 151 Magnetism from Coulomb’s law and relativity 301 152 Relativistic invariance of electrodynamics 305 153 Review of Lorentz transformations 305 1531 Implications for Newtonian mechanics 307 154 Scalar and vector fields 309 155 The derivative operator 312 156 Lorentz scalars and vectors 315 157 The four-current J 317 1571 Charge conservation and the four-current J 318 158 The four-potential A 319 1581 Gauge invariance 322 159 Wave equation for the four-vector A 324 1591 Why work with V and A? 327 1510 The electromagnetic tensor F 328 15101 Tensors 328 15102 The electromagnetic field tensor F 332 16 Optics I: Geometric Optics Revisited 336 161 Geometric or ray optics 336 162 Brief history of c 338 163 Some highlights of geometric optics 340 164 The law of reflection from Fermat’s principle 343 165 Snell’s law from Fermat’s principle 344 166 Reflection off a curved surface by Fermat 346 167 Elliptical mirrors and Fermat’s principle 349 168 Parabolic mirrors 352 17 Optics II: More Mirrors and Lenses 355 171 Spherical approximations to parabolic mirrors 355 172 Image formation: geometric optics 357 1721 A midlife crisis 359 173 Image formation by Fermat’s principle 360 174 Tricky cases 364 1741 Fermat’s principle for virtual focal points 365 1742 Ray optics for virtual images 366 175 Lenses `a la Fermat 368 176 Principle of least action 370 177 The eye 372 18 Wave Theory of Light 377 181 Interference of waves 381 182 Adding waves using real numbers 383 183 Adding waves with complex numbers 385 184 Analysis of interference 388 185 Diffraction grating 394 186 Single-slit diffraction 397 187 Understanding reflection and crystal diffraction 398 188 Light incident on an oil slick 401 1881 Normal incidence 401 1882 Oblique incidence 404 19 Quantum Mechanics: The Main Experiment 406 191 Double-slit experiment with light 407 192 Trouble with Maxwell 407 193 Digression on photons 412 1931 Photoelectric effect 412 1932 Compton effect 414 194 Matter waves 416 195 Photons versus electrons 420 196 The Heisenberg uncertainty principle 422 1961 There are no states of well-defined position and momentum 423 1962 Heisenberg microscope 427 197 Let there be light 430 198 The wave function 435 199 Collapse of the wave function 438 1910 Summary 439 20 TheWave Function and Its Interpretation 442 201 Probability in classical and quantum mechanics 446 202 Getting to know 451 203 Statistical concepts: mean and uncertainty 456 21 Quantization and Measurement 460 211 More on momentum states 462 212 Single-valuedness and quantization of momentum 464 2121 Quantization 467 2122 The integral of p(x) 468 213 Measurement postulate: momentum 469 2131 An example solvable by inspection 476 2132 Using a normalized 478 214 Finding A(p) by computation 480 215 More on Fourier’s theorems 486 216 Measurement postulate: general 491 217 More than one variable 493 22 States of Definite Energy 495 221 Free particle on a ring 500 2211 Analysis of energy levels: degeneracy 503 222 Thinking inside the box 507 2221 Particle in a well 507 2222 The box: an exact solution 516 223 Energy measurement in the box 521 23 Scattering and Dynamics 524 231 Quantum scattering 524 2311 Scattering for E > V0 526 2312 Scattering for E < V0 530 232 Tunneling 531 233 Quantum dynamics 533 2331 A solution of the time-dependent Schr¨odinger equation 535 2332 Derivation of the particular solution E(x, t) 536 234 Special properties of the product solution 538 235 General solution for time evolution 541 2351 Time evolution: a more complicated example 545 24 Summary and Outlook 550 241 Postulates: first pass 550 242 Refining the postulates 554 2421 Toward a compact set of postulates 555 2422 Eigenvalue problem 556 2423 The Dirac delta function and the operator X 558 243 Postulates: final 565 244 Many particles, bosons, and fermions 566 2441 Identical versus indistinguishable 567 2442 Implications for atomic structure 574 245 Energy-time uncertainty principle 576 246 What next? 583 Exercises 585 Problem Set 1, for Chapters 1 and 2 585 Problem Set 2, for Chapters 3 and 4 588 Problem Set 3, for Chapters 5 and 6 591 Problem Set 4, for Chapter 7 595 Problem Set 5, for Chapters 8 and 9 599 Problem Set 6, for Chapter 10 604 Problem Set 7, for Chapters 11, 12, and 13 609 Problem Set 8, for Chapters 14 and 15 613 Problem Set 9, for Chapters 16, 17, and 18 617 Problem Set 10, for Chapters 19 and 20 622 Problem Set 11, for Chapters 21 and 22 624 Problem Set 12, for Chapters 23 and 24 626 Answers to Exercises 629 Problem Set 1, for Chapters 1 and 2 629 Problem Set 2, for Chapters 3 and 4 631 Problem Set 3, for Chapters 5 and 6 633 Problem Set 4, for Chapter 7 635 Problem Set 5, for Chapters 8 and 9 637 Problem Set 6, for Chapter 10 640 Problem Set 7, for Chapters 11, 12, and 13 642 Problem Set 8, for Chapters 14 and 15 644 Problem Set 9, for Chapters 16, 17, and 18 646 Problem Set 10, for Chapters 19 and 20 648 Problem Set 11, for Chapters 21 and 22 649 Problem Set 12, for Chapters 23 and 24 650 Constants 653