UNDERSTANDING PHYSICS: LIGHT, MAGNETISM & ELECTRICITY
13 LCR CIRCUITS AND DISPLACEMENT CURRENT ANALYSIS OF LCR RESULTS TRANSIENTS AND THE COMPLEMENTARY SOLUTION POWER OF THE COMPLEX NUMBERS DISPLACEMENT CURRENT 14 ELECTROMAGNETIC WAVES THE WAVE EQUATION RESTRICTED MAXWELL EQUATIONS IN VACUUM MAXWELL EQUATIONS INVOLVING IN?NITESIMAL CUBES MAXWELL EQUATIONS INVOLVING IN?NITESIMAL LOOPS THE WAVE! SINUSOIDAL SOLUTION TO THE WAVE EQUATION ENERGY IN THE ELECTROMAGNETIC WAVE ORIGIN OF ELECTROMAGNETIC WAVES MAXWELL EQUATIONS—THE GENERAL CASE (OPTIONAL) CONSEQUENCES FOR THE RESTRICTED E AND B FROM MICROSCOPIC TO MACROSCOPIC (OPTIONAL) MAXWELL EQUATIONS INVOLVING CUBES MAXWELL EQUATIONS INVOLVING LOOPS 15 ELECTROMAGNETISM AND RELATIVITY MAGNETISM FROM COULOMB’S LAW AND RELATIVITY RELATIVISTIC INVARIANCE OF ELECTRODYNAMICS REVIEW OF LORENTZ TRANSFORMATIONS IMPLICATIONS FOR NEWTONIAN MECHANICS SCALAR AND VECTOR ?ELDS THE DERIVATIVE OPERATOR LORENTZ SCALARS AND VECTORS THE FOUR-CURRENT J CHARGE CONSERVATION AND THE FOUR-CURRENT J THE FOUR-POTENTIAL A GAUGE INVARIANCE WAVE EQUATION FOR THE FOUR-VECTOR A WHY WORK WITH V AND A? 15 10 THE ELECTROMAGNETIC TENSOR F 15 10 1 TENSORS 15 10 2 THE ELECTROMAGNETIC ?ELD TENSOR F 16 OPTICS I: GEOMETRIC OPTICS REVISITED GEOMETRIC OR RAY OPTICS BRIEF HISTORY OF C SOME HIGHLIGHTS OF GEOMETRIC OPTICS THE LAW OF RE?ECTION FROM FERMAT’S PRINCIPLE SNELL’S LAW FROM FERMAT’S PRINCIPLE RE?ECTION OFF A CURVED SURFACE BY FERMAT ELLIPTICAL MIRRORS AND FERMAT’S PRINCIPLE PARABOLIC MIRRORS 17 OPTICS II: MORE MIRRORS AND LENSES SPHERICAL APPROXIMATIONS TO PARABOLIC MIRRORS IMAGE FORMATION: GEOMETRIC OPTICS A MIDLIFE CRISIS IMAGE FORMATION BY FERMAT’S PRINCIPLE TRICKY CASES FERMAT’S PRINCIPLE FOR VIRTUAL FOCAL POINTS RAY OPTICS FOR VIRTUAL IMAGES LENSES `A LA FERMAT PRINCIPLE OF LEAST ACTION THE EYE 18 WAVE THEORY OF LIGHT INTERFERENCE OF WAVES ADDING WAVES USING REAL NUMBERS ADDING WAVES WITH COMPLEX NUMBERS ANALYSIS OF INTERFERENCE DIFFRACTION GRATING SINGLE-SLIT DIFFRACTION UNDERSTANDING RE?ECTION AND CRYSTAL DIFFRACTION LIGHT INCIDENT ON AN OIL SLICK NORMAL INCIDENCE OBLIQUE INCIDENCE 19 QUANTUM MECHANICS: THE MAIN EXPERIMENT DOUBLE-SLIT EXPERIMENT WITH LIGHT TROUBLE WITH MAXWELL DIGRESSION ON PHOTONS PHOTOELECTRIC EFFECT COMPTON EFFECT MATTER WAVES PHOTONS VERSUS ELECTRONS THE HEISENBERG UNCERTAINTY PRINCIPLE THERE ARE NO STATES OF WELL-DE?NED POSITION AND MOMENTUM HEISENBERG MICROSCOPE LET THERE BE LIGHT THE WAVE FUNCTION ? COLLAPSE OF THE WAVE FUNCTION 19 10 SUMMARY 20 THE WAVE FUNCTION AND ITS INTERPRETATION PROBABILITY IN CLASSICAL AND QUANTUM MECHANICS GETTING TO KNOW ? STATISTICAL CONCEPTS: MEAN AND UNCERTAINTY 21 QUANTIZATION AND MEASUREMENT MORE ON MOMENTUM STATES SINGLE-VALUEDNESS AND QUANTIZATION OF MOMENTUM QUANTIZATION THE INTEGRAL OF ?P(X) MEASUREMENT POSTULATE: MOMENTUM AN EXAMPLE SOLVABLE BY INSPECTION USING A NORMALIZED ? FINDING A(P) BY COMPUTATION MORE ON FOURIER’S THEOREMS MEASUREMENT POSTULATE: GENERAL MORE THAN ONE VARIABLE