EXPERIMENTAL PHYSICS: A TEXT-BOOK OF MECHANICS, HEAT, SOUND AND LIGHT

By Z. DIZIL

CONTENTS INTRODUCTION ELECTROMAGNETIC WAVES RADIATION PULSES WAVE DIFFRACTION BLACKBODY SPECTRUM: ORIGIN OF THE QUANTUM THEORY PHOTOELECTRIC EFFECT BOHR THEORY DE BROGLIE WAVES THE SCHRÖDINGER EQUATION AND PROBABILITY WAVES MEASUREMENT AND SUPERPOSITION STATES WHAT IS TRULY STRANGE ABOUT QUANTUM MECHANICS: SUPERPOSITION STATES THE EPR PARADOX AND BELL’S THEOREM SUMMARY APPENDIX: BLACKBODY SPECTRUM BOX NORMALIZATION WITH FIELD NODES ON THE WALLS PERIODIC BOUNDARY CONDITIONS RAYLEIGH-JEANS LAW PLANCK’S SOLUTION APPROACH TO EQUILIBRIUM PROBLEMS MATHEMATICAL PRELIMINARIES COMPLEX FUNCTION OF A REAL VARIABLE FUNCTIONS AND TAYLOR SERIES FUNCTIONS OF ONE VARIABLE SCALAR FUNCTIONS OF THREE VARIABLES VECTOR FUNCTIONS OF THREE VARIABLES VECTOR CALCULUS PROBABILITY DISTRIBUTIONS FOURIER TRANSFORMS DIRAC DELTA FUNCTION FREE-PARTICLE SCHRÖDINGER EQUATION: WAVE PACKETS ELECTROMAGNETIC WAVE EQUATION: PULSES SCHRÖDINGER’S EQUATION WAVE PACKETS FREE-PARTICLE PROPAGATOR SCHRÖDINGER’S EQUATION WITH POTENTIAL ENERGY: INTRODUCTION TO OPERATORS HAMILTONIAN OPERATOR TIME-INDEPENDENT SCHRÖDINGER EQUATION APPENDIX: SCHRÖDINGER EQUATION IN THREE DIMENSIONS POSTULATES AND BASIC ELEMENTS OF QUANTUM MECHANICS: PROPERTIES OF OPERATORS HERMITIAN OPERATORS: EIGENVALUES AND EIGENFUNCTIONS EIGENVALUES REAL ORTHOGONALITY COMPLETENESS CONTINUOUS EIGENVALUES RELATIONSHIP BETWEEN OPERATORS COMMUTATOR OF OPERATORS UNCERTAINTY PRINCIPLE EXAMPLES OF OPERATORS BACK TO THE SCHRÖDINGER EQUATION HOW TO SOLVE THE TIME-DEPENDENT SCHRÖDINGER EQUATION QUANTUM-MECHANICAL PROBABILITY CURRENT DENSITY OPERATOR DYNAMICS SUM OF TWO INDEPENDENT QUANTUM SYSTEMS MEASUREMENTS IN QUANTUM MECHANICS: “COLLAPSE” OF THE WAVE FUNCTION APPENDIX: FROM DISCRETE TO CONTINUOUS EIGENVALUES PROBLEMS IN ONE-DIMENSION: GENERAL CONSIDERATIONS, IN?NITE WELL POTENTIAL, PIECEWISE CONSTANT POTENTIALS, AND DELTA FUNCTION POTENTIALS GENERAL CONSIDERATIONS POTENTIALS IN WHICH V X/ > 0 AND V ?1/ 0 POTENTIALS IN WHICH V X/ > 0 AND V 1/ WHILE V 1/ 1 WHILE V 1/ D W > 0 POTENTIALS IN WHICH V X/ > 0 AND V ?1/ 1 POTENTIALS IN WHICH V X/ < 0 AND V ?1/ 0 IN?NITE WELL POTENTIAL WELL LOCATED BETWEEN A=2 AND A=2 WELL LOCATED BETWEEN 0 AND A POSITION AND MOMENTUM DISTRIBUTIONS QUANTUM DYNAMICS PIECEWISE CONSTANT POTENTIALS POTENTIAL STEP SQUARE WELL POTENTIAL POTENTIAL BARRIER DELTA FUNCTION POTENTIAL WELL AND BARRIER SQUARE WELL WITH E < 0 BARRIER WITH E > 0 APPENDIX: PERIODIC POTENTIALS BLOCH STATES ADVANCED PROBLEMS SIMPLE HARMONIC OSCILLATOR: ONE DIMENSION CLASSICAL PROBLEM QUANTUM PROBLEM EIGENFUNCTIONS AND EIGENENERGIES TIME-DEPENDENT PROBLEMS PROBLEMS IN TWO AND THREE-DIMENSIONS: GENERAL CONSIDERATIONS SEPARABLE HAMILTONIANS IN X; Y; Z FREE PARTICLE TWO- AND THREE-DIMENSIONAL IN?NITE WELLS SHO IN TWO AND THREE DIMENSIONS GENERAL HAMILTONIANS IN TWO AND THREE DIMENSIONS CENTRAL FORCES AND ANGULAR MOMENTUM ANGULAR MOMENTUM PHYSICAL INTERPRETATION OF THE SPHERICAL HARMONICS APPENDIX: CLASSICAL ANGULAR DISTRIBUTION SPHERICALLY SYMMETRIC POTENTIALS: RADIAL EQUATION RADIAL MOMENTUM GENERAL SOLUTION OF THE SCHRÖDINGER EQUATION FOR SPHERICALLY SYMMETRIC POTENTIALS BOUNDARY CONDITIONS IN?NITE SPHERICAL WELL POTENTIAL FINITE SPHERICAL WELL POTENTIAL: BOUND STATES BOUND STATE COULOMB PROBLEM (HYDROGEN ATOM) 3-D ISOTROPIC HARMONIC OSCILLATOR APPENDIX: LAGUERRE POLYNOMIALS DIRAC NOTATION VECTOR SPACES AND DIRAC NOTATION VECTOR SPACES HILBERT SPACE SCHRÖDINGER’S EQUATION IN MOMENTUM SPACE SIMPLE HARMONIC OSCILLATOR COHERENT STATE ANGULAR MOMENTUM OPERATOR SOLVING PROBLEMS USING DIRAC NOTATION HYDROGEN ATOM HARMONIC OSCILLATOR LIMITED SUBSPACES CONNECTION WITH LINEAR ALGEBRA TIME DEPENDENCE APPENDIX A: MATRIX PROPERTIES APPENDIX B: SPHERICAL HARMONICS IN DIRAC NOTATION SPIN CLASSICAL MAGNETIC MOMENT SPIN MAGNETIC MOMENT SPIN-ORBIT COUPLING IN HYDROGEN COUPLING OF ORBITAL AND SPIN ANGULAR MOMENTUM SPIN AND STATISTICS (A) REVIEW OF BASIC CONCEPTS (B) FEYNMAN PATH INTEGRAL APPROACH (C) BELL’S INEQUALITIES REVISITED REVIEW OF BASIC CONCEPTS POSTULATES WAVE FUNCTION APPROACH QUANTUM-MECHANICAL CURRENT DENSITY OPERATORS MEASUREMENT IN QUANTUM MECHANICS HEISENBERG REPRESENTATION FEYNMAN PATH-INTEGRAL APPROACH BELL’S THEOREM PROOF OF BELL’S THEOREM ELECTRON SPIN MEASUREMENTS PHOTON POLARIZATION MEASUREMENTS QUANTUM TELEPORTATION WHY THE BIG FUSS? APPENDIX: EQUIVALENCE OF FEYNMAN PATH INTEGRAL AND SCHRÖDINGER EQUATION PERTURBATION THEORY NON-DEGENERATE PERTURBATION THEORY EXAMPLES DEGENERATE PERTURBATION THEORY VARIATIONAL APPROACH COMBINING PERTURBATION THEORY AND THE VARIATIONAL APPROACH HELIUM ATOM WKB APPROXIMATION WKB WAVE FUNCTIONS CONNECTION FORMULAS BOUND STATE PROBLEMS APPENDIX: CONNECTION FORMULAS SCATTERING: 1-D STEADY-STATE APPROACH TIME-DEPENDENT APPROACH E0 > V0 FOR STEP POTENTIAL E0 < V0 FOR STEP POTENTIAL SCATTERING: 3-D CLASSICAL SCATTERING QUANTUM SCATTERING METHOD OF PARTIAL WAVES BORN APPROXIMATION APPENDIX A: FREE PARTICLE SOLUTION IN SPHERICAL COORDINATES APPENDIX B: HARD SPHERE SCATTERING WHEN KA 1 SYMMETRY AND TRANSFORMATIONS: ROTATION MATRICES ACTIVE VERSUS PASSIVE TRANSFORMATIONS PASSIVE AND ACTIVE TRANSLATIONS PASSIVE AND ACTIVE ROTATIONS EXTENSION TO THREE DIMENSIONS QUANTUM MECHANICS TRANSLATION OPERATOR ROTATION OPERATOR EXTENSION TO INCLUDE SPIN ANGULAR MOMENTUM TRANSFORMATION OF OPERATORS ROTATIONS: EXAMPLES ROTATION MATRIX ROTATION MATRICES APPENDIX: FINITE TRANSLATIONS AND ROTATIONS ADDITION OF ANGULAR MOMENTA, CLEBSCH-GORDAN COEF?CIENTS, VECTOR AND TENSOR OPERATORS, WIGNER-ECKART THEOREM ADDITION OF ANGULAR MOMENTA AND CLEBSCH-GORDAN COEF?CIENTS VECTOR AND TENSOR OPERATORS WIGNER-ECKART THEOREM APPENDIX: PROOF OF THE WIGNER-ECKART THEOREM HYDROGEN ATOM WITH SPIN IN EXTERNAL FIELDS ENERGY LEVELS OF HYDROGEN UNPERTURBED HAMILTONIAN RELATIVISTIC MASS CORRECTION SPIN INCLUDED SPIN–ORBIT INTERACTION DARWIN TERM TOTAL FINE STRUCTURE LAMB SHIFT HYPER?NE STRUCTURE ADDITION OF A MAGNETIC FIELD ADDITION OF AN ELECTRIC FIELD MULTI-ELECTRON ATOMS IN A MAGNETIC FIELD: VECTOR MODEL ZEEMAN SPLITTING MUCH GREATER THAN SPIN-ORBIT SPLITTING SPIN-ORBIT SPLITTING MUCH GREATER THAN ZEEMAN SPLITTING APPENDIX A: RADIAL INTEGRALS FOR HYDROGEN APPENDIX B: HYPER?NE INTERACTIONS HYPER?NE SPLITTING ZEEMAN SPLITTING CONTRIBUTION TO THE HYPER?NE SPLITTING FROM NON-CONTACT INTERACTION TERMS INTERACTION REPRESENTATION SPIN 1/2 QUANTUM SYSTEM IN A MAGNETIC FIELD ANALYTIC SOLUTIONS TWO-LEVEL ATOM ROTATING-WAVE OR RESONANCE APPROXIMATION FIELD-INTERACTION REPRESENTATION DENSITY MATRIX FOR A SINGLE ATOM MAGNETIC BLOCH EQUATIONS OPTICAL BLOCH EQUATIONS SELECTION RULES FOR ELECTRIC DIPOLE AND MAGNETIC DIPOLE TRANSITIONS APPENDIX: INTERACTION OF AN ATOM WITH A THERMAL BATH APPROXIMATION TECHNIQUES IN TIME-DEPENDENT PROBLEMS TIME-DEPENDENT PERTURBATION THEORY ADIABATIC APPROXIMATION A SIMPLE EXAMPLE SUDDEN APPROXIMATION DECAY OF A DISCRETE STATE INTO A CONTINUUM OF STATES: FERMI’S GOLDEN RULE DISCRETE STATE COUPLED TO A CONTINUUM PHOTOIONIZATION SPONTANEOUS DECAY BOUNDED CONTINUUM ZENO PARADOX AND ZENO EFFECT