PROBLEMS IN UNDERGRADUATE PHYSICS: MOLECULAR AND NUCLEAR PHYSICS
CONTENTS MATHEMATICAL PART INTRODUCTION ELEMENTS FROM THE THEORY OF LINEAR SPACES COORDINATE TRANSFORMATIONS INNER PRODUCT: METRIC TENSORS OPERATIONS OF TENSORS THE CASE OF EUCLIDIAN GEOMETRY THE LORENTZ GEOMETRY LORENTZ TRANSFORMATIONS ALGEBRAIC DETERMINATION OF THE LORENTZ TRANSFORMATION L(?) THE KINEMATIC INTERPRETATION OF THE GENERAL LORENTZ TRANSFORMATION RELATIVISTIC PARALLELISM OF SPACE AXES THE KINEMATIC INTERPRETATION OF LORENTZ TRANSFORMATION THE GEOMETRY OF THE BOOST CHARACTERISTIC FRAMES OF FOUR-VECTORS PROPER FRAME OF A TIMELIKE FOUR-VECTOR CHARACTERISTIC FRAME OF A SPACELIKE FOUR-VECTOR PARTICLE FOUR-VECTORS THE CENTER SYSTEM (CS) OF A SYSTEM OF PARTICLE FOUR-VECTORS THE STRUCTURE OF THE THEORIES OF PHYSICS THE ROLE OF PHYSICS THE STRUCTURE OF A THEORY OF PHYSICS PHYSICAL QUANTITIES AND REALITY OF A THEORY OF PHYSICS INERTIAL OBSERVERS GEOMETRIZATION OF THE PRINCIPLE OF RELATIVITY PRINCIPLE OF INERTIA THE COVARIANCE PRINCIPLE RELATIVITY AND THE PREDICTIONS OF A THEORY NEWTONIAN PHYSICS NEWTONIAN KINEMATICS MASS POINT SPACE TIME NEWTONIAN INERTIAL OBSERVERS DETERMINATION OF NEWTONIAN INERTIAL OBSERVERS MEASUREMENT OF THE POSITION VECTOR GALILEO PRINCIPLE OF RELATIVITY GALILEO TRANSFORMATIONS FOR SPACE AND TIME: NEWTONIAN PHYSICAL QUANTITIES GALILEO COVARIANT PRINCIPLE: PART I GALILEO PRINCIPLE OF COMMUNICATION NEWTONIAN PHYSICAL QUANTITIES: THE COVARIANCE PRINCIPLE GALILEO COVARIANCE PRINCIPLE: PART II NEWTONIAN COMPOSITION LAW OF VECTORS NEWTONIAN DYNAMICS LAW OF CONSERVATION OF LINEAR MOMENTUM THE FOUNDATION OF SPECIAL RELATIVITY LIGHT AND THE GALILEO’S PRINCIPLE OF RELATIVITY THE EXISTENCE OF NON-NEWTONIAN PHYSICAL QUANTITIES THE LIMIT OF SPECIAL RELATIVITY TO NEWTONIAN PHYSICS THE PHYSICAL ROLE OF THE SPEED OF LIGHT THE PHYSICAL DE?NITION OF SPACETIME THE EVENTS THE GEOMETRY OF SPACETIME STRUCTURES IN MINKOWSKI SPACE THE LIGHT CONE WORLD LINES CURVES IN MINKOWSKI SPACE GEOMETRIC DE?NITION OF RELATIVISTIC INERTIAL OBSERVERS (RIO) PROPER TIME THE PROPER FRAME OF A RIO PROPER OR REST SPACE SPACETIME DESCRIPTION OF MOTION THE PHYSICAL DE?NITION OF A RIO RELATIVISTIC MEASUREMENT OF THE POSITION VECTOR THE PHYSICAL DE?NITION OF A LRIO THE EINSTEIN PRINCIPLE OF RELATIVITY THE EQUATION OF LORENTZ ISOMETRY THE LORENTZ COVARIANCE PRINCIPLE LORENTZ COVARIANCE PRINCIPLE: PART I LORENTZ COVARIANCE PRINCIPLE PART II RULES FOR CONSTRUCTING LORENTZ TENSORS POTENTIAL RELATIVISTIC PHYSICAL QUANTITIES UNIVERSAL SPEEDS AND THE LORENTZ TRANSFORMATION THE PHYSICS OF THE POSITION FOUR-VECTOR THE CONCEPTS OF SPACE AND TIME IN SPECIAL RELATIVITY MEASUREMENT OF SPATIAL AND TEMPORAL DISTANCE IN SPECIAL RELATIVITY RELATIVISTIC DE?NITION OF SPATIAL AND TEMPORAL DISTANCES TIMELIKE POSITION FOUR-VECTOR: MEASUREMENT OF TEMPORAL DISTANCE SPACELIKE POSITION FOUR-VECTOR: MEASUREMENT OF SPATIAL DISTANCE THE GENERAL CASE THE REALITY OF LENGTH CONTRACTION AND TIME DILATION THE RIGID ROD OPTICAL IMAGES IN SPECIAL RELATIVITY HOW TO SOLVE PROBLEMS INVOLVING SPATIAL AND TEMPORAL DISTANCE A BRIEF SUMMARY OF THE LORENTZ TRANSFORMATION PARALLEL AND NORMAL DECOMPOSITION OF LORENTZ TRANSFORMATION METHODOLOGIES OF SOLVING PROBLEMS INVOLVING BOOSTS THE ALGEBRAIC METHOD THE GEOMETRIC METHOD RELATIVISTIC KINEMATICS RELATIVISTIC MASS POINT RELATIVISTIC COMPOSITION OF 3-VECTORS RELATIVE FOUR-VECTORS THE 3-VELOCITY SPACE THOMAS PRECESSION FOUR-ACCELERATION THE FOUR-ACCELERATION CALCULATING ACCELERATED MOTIONS HYPERBOLIC MOTION OF A RELATIVISTIC MASS PARTICLE GEOMETRIC REPRESENTATION OF HYPERBOLIC MOTION SYNCHRONIZATION EINSTEIN SYNCHRONIZATION K ?CALCULUS RIGID MOTION OF MANY RELATIVISTIC MASS POINTS RIGID MOTION AND HYPERBOLIC MOTION BORN SYNCHRONIZATION OF LRIO SYNCHRONIZATION OF CHRONOMETRY THE KINEMATICS IN THE LCF THE CASE OF THE GRAVITATIONAL FIELD GENERAL ONE DIMENSIONAL RIGID MOTION THE CASE OF HYPERBOLIC MOTION ROTATIONAL RIGID MOTION THE TRANSITIVE PROPERTY OF THE RIGID ROTATIONAL MOTION THE ROTATING DISC THE KINEMATICS OF RELATIVISTIC OBSERVERS CHRONOMETRY AND THE SPATIAL LINE ELEMENT THE ROTATING DISK DE?NITION OF THE ROTATING DISK FOR A RIO THE LOCALLY RELATIVISTIC INERTIAL OBSERVER (LRIO) THE ACCELERATED OBSERVER THE GENERALIZATION OF LORENTZ TRANSFORMATION AND THE ACCELERATED OBSERVERS THE GENERALIZED LORENTZ TRANSFORMATION THE SPECIAL CASE U0(L?, X?) = U1(L?, X?) = U(X?) EQUATION OF MOTION IN A GRAVITATIONAL FIELD THE LIMITS OF SPECIAL RELATIVITY EXPERIMENT 1: THE GRAVITATIONAL REDSHIFT EXPERIMENT 2: THE GRAVITATIONAL TIME DILATION EXPERIMENT 3: THE CURVATURE OF SPACETIME PARADOXES VARIOUS PARADOXES MASS: FOUR-MOMENTUM THE (RELATIVISTIC) MASS THE FOUR-MOMENTUM OF A REMAP THE FOUR-MOMENTUM OF PHOTONS (LUXONS) THE FOUR-MOMENTUM OF PARTICLES THE SYSTEM OF NATURAL UNITS RELATIVISTIC REACTIONS REPRESENTATION OF PARTICLE REACTIONS THE SUM OF PARTICLE FOUR-VECTORS THE RELATIVISTIC TRIANGLE INEQUALITY WORKING WITH FOUR-MOMENTA SPECIAL COORDINATE FRAMES IN THE STUDY OF RELATIVISTIC COLLISIONS THE GENERIC REACTION A + B ?C THE PHYSICS OF THE GENERIC REACTION THRESHOLD OF A REACTION TRANSFORMATION OF ANGLES RADIATIVE TRANSITIONS REACTIONS WITH TWO PHOTON FINAL STATE ELASTIC COLLISIONS: SCATTERING FOUR-FORCE THE FOUR-FORCE INERTIAL FOUR-FORCE AND FOUR-POTENTIAL THE VECTOR FOUR-POTENTIAL THE LAGRANGIAN FORMALISM FOR INERTIAL FOUR-FORCES MOTION IN A CENTRAL POTENTIAL MOTION OF A ROCKET THE FRENET-SERRET FRAME IN MINKOWSKI SPACE THE PHYSICAL BASIS THE GENERIC INERTIAL FOUR-FORCE APPLICATIONS IRREDUCIBLE DECOMPOSITIONS DECOMPOSITIONS WRITING A TENSOR OF VALENCE (0,2) AS A MATRIX THE IRREDUCIBLE DECOMPOSITION WRT A NON-NULL VECTOR DECOMPOSITION IN A EUCLIDEAN SPACE EN 1+3 DECOMPOSITION IN MINKOWSKI SPACE 1+1+2 DECOMPOSITION WRT A PAIR OF A TIMELIKE FOUR-VECTOR AND A NON-NULL FOUR-VECTOR THE ELECTROMAGNETIC FIELD MAXWELL EQUATIONS IN NEWTONIAN PHYSICS THE ELECTROMAGNETIC POTENTIAL THE EQUATION OF CONTINUITY THE ELECTROMAGNETIC FOUR-POTENTIAL THE ELECTROMAGNETIC FIELD TENSOR FIJ THE TRANSFORMATION OF THE FIELDS MAXWELL EQUATIONS IN TERMS OF FIJ THE INVARIANTS OF THE ELECTROMAGNETIC FIELD THE PHYSICAL SIGNI?CANCE OF THE ELECTROMAGNETIC INVARIANTS THE CASE Y = 0 THE CASE Y ?= 0 MOTION OF A CHARGE IN AN ELECTROMAGNETIC FIELD: THE LORENTZ FORCE MOTION OF A CHARGE IN A HOMOGENEOUS ELECTROMAGNETIC FIELD THE CASE OF A HOMOGENEOUS ELECTRIC FIELD THE CASE OF A HOMOGENEOUS MAGNETIC FIELD THE CASE OF TWO HOMOGENEOUS FIELDS OF EQUAL STRENGTH AND PERPENDICULAR DIRECTIONS THE CASE OF HOMOGENEOUS AND PARALLEL FIELDS E ?B THE RELATIVISTIC ELECTRIC AND MAGNETIC FIELDS THE LEVI CIVITA TENSOR DENSITY THE CASE OF VACUUM THE ELECTROMAGNETIC THEORY FOR A GENERAL MEDIUM THE ELECTRIC AND MAGNETIC MOMENTS MAXWELL EQUATIONS FOR A GENERAL MEDIUM THE 1 + 3 DECOMPOSITION OF MAXWELL EQUATIONS THE FOUR-CURRENT OF CONDUCTIVITY AND OHM’S LAW THE CONTINUITY EQUATION J A;A = 0 FOR AN ISOTROPIC MATERIAL THE ELECTROMAGNETIC FIELD IN A HOMOGENEOUS AND ISOTROPIC MEDIUM ELECTRIC CONDUCTIVITY AND THE PROPAGATION EQUATION FOR DA THE GENERALIZED OHM’S LAW THE ENERGY MOMENTUM TENSOR OF THE ELECTROMAGNETIC FIELD THE 1 + 3 DECOMPOSITION OF THE TENSOR TAB THE ELECTROMAGNETIC FIELD OF A MOVING CHARGE THE INVARIANTS THE FIELDS EI, BI THE LIÉNARD–WIECHERT POTENTIALS AND THE FIELDS E, B SPECIAL RELATIVITY AND PRACTICAL APPLICATIONS THE SYSTEMS OF UNITS SI AND GAUSS IN ELECTROMAGNETISM RELATIVISTIC ANGULAR MOMENTUM MATHEMATICAL PRELIMINARIES 1 + 3 DECOMPOSITION OF A BIVECTOR XAB THE DERIVATIVE OF THE BIVECTOR XAB ALONG THE VECTOR PA THE ANGULAR MOMENTUM IN SPECIAL RELATIVITY THE ANGULAR MOMENTUM IN NEWTONIAN THEORY THE ANGULAR MOMENTUM OF A PARTICLE IN SPECIAL RELATIVITY THE INTRINSIC ANGULAR MOMENTUM: THE SPIN VECTOR THE MAGNETIC DIPOLE THE RELATIVISTIC SPIN MOTION OF A PARTICLE WITH SPIN IN A HOMOGENEOUS ELECTROMAGNETIC FIELD TRANSFORMATION OF MOTION IN THE COVARIANT LORENTZ TRANSFORMATION DE?NITION OF THE LORENTZ TRANSFORMATION COMPUTATION OF THE COVARIANT LORENTZ TRANSFORMATION THE ACTION OF THE COVARIANT LORENTZ TRANSFORMATION ON THE COORDINATES THE INVARIANT LENGTH OF A FOUR-VECTOR THE FOUR TYPES OF THE LORENTZ TRANSFORMATION VIEWED AS SPACETIME RE?ECTIONS RELATIVISTIC COMPOSITION RULE OF 4-VECTORS COMPUTATION OF THE COMPOSITE FOUR-VECTOR THE RELATIVISTIC COMPOSITION RULE FOR 3-VELOCITIES RIEMANNIAN GEOMETRY AND SPECIAL RELATIVITY THE RELATIVISTIC RULE FOR THE COMPOSITION OF 3-ACCELERATIONS THE COMPOSITION OF LORENTZ TRANSFORMATIONS NULL TRIADS AND PROPER LORENTZ TRANSFORMATION TETRADS AND THE LORENTZ TRANSFORMATION THE NULL TRIAD THE ALLCOCK APPROACH THE TWO NULL VECTOR APPROACH (SYNGE) THE CHARACTERISTIC TETRAD OF A NULL TRIAD THE NULL TETRAD THE PROPER ORTHOCHRONOUS LORENTZ TRANSFORMATION IN TERMS OF THE NULL TETRAD THE SPECIAL LORENTZ TRANSFORMATION IN TERMS OF BIVECTORS GEOMETRIC DESCRIPTION OF RELATIVISTIC INTERACTIONS COLLISIONS AND GEOMETRY GEOMETRIC DESCRIPTION OF COLLISIONS IN NEWTONIAN PHYSICS GEOMETRIC DESCRIPTION OF RELATIVISTIC REACTIONS THE GENERAL GEOMETRIC RESULTS THE 1 + 3 DECOMPOSITION OF A PARTICLE FOUR-VECTOR WRT A TIMELIKE FOUR-VECTOR THE SYSTEM OF TWO TO ONE PARTICLE FOUR-VECTORS THE TRIANGLE FUNCTION OF A SYSTEM OF TWO PARTICLE FOUR-VECTORS EXTREME VALUES OF THE FOUR-VECTORS (A ± B)2 THE SYSTEM AA, BA, (A + B)A OF PARTICLE FOUR-VECTORS IN CS THE SYSTEM AA, BA, (A + B)A IN THE LAB THE RELATIVISTIC SYSTEM AA + BA ?CA + DA THE REACTION B ??C + D WAVES IN SPECIAL RELATIVITY THE DISTURBANCE WAVES IN NEWTONIAN PHYSICS PLANE WAVES SPHERICAL WAVES LINEAR SUPERPOSITION OF WAVES PERIOD AND WAVELENGTH OF A WAVE RELATIVISTIC WAVES THE FREQUENCY FOUR-VECTOR THE DOPPLER SHIFT THE ABERRATION OF THE WAVE VECTOR ELECTROMAGNETIC WAVES IN A HOMOGENEOUS AND ISOTROPIC MEDIUM CENTER OF MOMENTUM OF A SYSTEM OF FREQUENCY FOUR VECTORS WAVES AND PARTICLES DEBROGLIE WAVES AND LIGHT DEBROGLIE WAVES AND PARTICLES THE PHYSICAL SYSTEM CONTINUUM THE MANIFOLD STRUCTURE THE GEOMETRY DE?NED BY THE METRIC THE STRUCTURE OF THE CLASSICAL THEORIES OF PHYSICS GEOMETRY AND THE COVARIANCE PRINCIPLE KINEMATICS: THE CONNECTING VECTOR A BRIEF DETOUR IN VECTOR ANALYSIS VECTOR FORMULATION TENSOR FORMULATION THE PHYSICS OF NEWTONIAN DEFORMABLE BODIES: NEWTONIAN FLUIDS THE KINEMATICS OF A NEWTONIAN DEFORMABLE BODY THE RELATIVE MOTION IN VECTOR FORMULATION THE RELATIVE VELOCITY OF LINEAR CONTINUA IN TENSOR NOTATION THE KINEMATIC INTERPRETATION OF NEWTONIAN RELATIVE VELOCITY NEWTONIAN KINEMATICS OF A LINEAR DEFORMABLE BODY IN TERMS OF THE CONNECTING VECTOR THE MOTION OF A LINEAR NEWTONIAN DEFORMABLE BODY IN TERMS OF GEOMETRY THE GEOMETRIZATION OF RIGID MOTION THE GEOMETRIZATION OF STRAIN MOTION THE GEOMETRY OF A GENERAL NEWTONIAN DEFORMABLE BODY THE STRESS TENSOR OF A LINEAR DEFORMABLE CONTINUUM BODY AND SURFACE FORCES THE PERFECT DEFORMABLE BODY THE IMPERFECT DEFORMABLE BODY CLASSI?CATION OF THE STRESS TENSOR OF LINEAR NEWTONIAN DEFORMABLE BODIES LONGITUDINAL STRESS SHEAR STRESS BULK OR VOLUME STRESS WORKED EXAMPLES ON THE NEWTONIAN STRESS TENSOR THE STRESS: STRAIN RELATION FOR ELASTIC NEWTONIAN DEFORMABLE BODIES THE STRESS RATE - STRAIN RELATION FOR A LINEAR ELASTIC ISOTROPIC BODY THE COEF?CIENTS N, K OF A LINEAR ELASTIC ISOTROPIC BODY A SECOND DERIVATION OF THE RATE OF STRAIN STRESS RELATION FORM HOOKE’S LAW THE DYNAMICS OF STRAIN MOTION OF AN ELASTIC BODY THE FORCE DUE TO A STRESS TENSOR NEWTON’S SECOND LAW IN TERMS OF THE DISPLACEMENT VECTOR KINEMATIC INTERPRETATION OF THE EQUATION OF MOTION OF THE STRAIN VECTOR IN A LINEAR ELASTIC ISOTROPIC NEWTONIAN BODY THE DYNAMIC EQUATION OF MOTION FOR A LINEAR ELASTIC ISOTROPIC NEWTONIAN BODY NEWTONIAN FLUIDS MATHEMATICAL CONCEPTS RELEVANT TO FLUIDS CLASSI?CATION OF FLUIDS AND FLUID FLOWS GEOMETRIC DESCRIPTION OF THE FLOW OF A FLUID CALCULATING THE STREAMLINES THE EQUATION OF CONTINUITY: CONSERVATION OF MASS THE EQUATION OF MOTION OF A PERFECT FLUID THE NAVIER STOKES EQUATION THE ELECTROMAGNETIC FIELD AS A NEWTONIAN VISCOUS FLUID A SHORT DETOUR TO THERMODYNAMICS AND HYDRODYNAMICS RELATIVISTIC FLUIDS IN SPECIAL RELATIVITY GENERAL DE?NITIONS THE 1 + 3 DECOMPOSITION WRT A GENERAL NON-NULL VECTOR QA THE EXTENDED METRIC AND THE BIVECTOR METRIC THE 1 + 3 DECOMPOSITION WRT THE FOUR-VELOCITY UA THE KINEMATICS OF A RELATIVISTIC FLUID THE DYNAMICS OF A RELATIVISTIC FLUID THE CASE OF A SINGLE PARTICLE THE CASE OF A SINGLE PARTICLE UNDER THE ACTION OF FORCES THE EQUATION OF MOTION OF A RELATIVISTIC FLUID THE DYNAMICAL PHYSICAL QUANTITIES OF A RELATIVISTIC FLUID THE DYNAMICAL EQUATIONS OF MOTION OF A RELATIVISTIC FLUID: A SIMPLI?ED APPROACH THE ENERGY MOMENTUM TENSOR OF A RELATIVISTIC VISCOUS FLUID THE ELECTROMAGNETIC FIELD IN VACUUM AS A RELATIVISTIC FLUID