TOPICS IN ATOMIC PHYSICS

By EMILY THOMPSON

CONTENTS CHAPTER BACKGROUND INTRODUCTION THE BOHR MODEL OF THE ATOM NUMERICAL VALUES AND THE FINE STRUCTURE CONSTANT ATOMIC DIMENSIONS—IS A0 A REASONABLE ATOMIC DIAMETER? LOCALIZING THE ELECTRON: IS A POINT PARTICLE REASONABLE? THE CLASSICAL RADIUS OF THE ELECTRON ATOMIC UNITS CHAPTER ANGULAR MOMENTUM COMMUTATORS ANGULAR MOMENTUM RAISING AND LOWERING OPERATORS ANGULAR MOMENTUM COMMUTATION RELATIONS WITH VECTOR OPERATORS MATRIX ELEMENTS OF VECTOR OPERATORS EIGENFUNCTIONS OF ORBITAL ANGULAR MOMENTUM OPERATORS SPIN THE STERN–GERLACH EXPERIMENT ANGULAR MOMENTUM—TWO SOURCES TWO SETS OF QUANTUM NUMBERS—UNCOUPLED AND COUPLED VECTOR MODEL OF ANGULAR MOMENTUM EXAMPLES OF CALCULATION OF THE CLEBSCH–GORDAN COEF?CIENTS HYPER?NE SPLITTING IN THE HYDROGEN ATOM THE QUANTUM MECHANICAL HYDROGEN ATOM THE RADIAL EQUATION FOR A CENTRAL POTENTIAL SOLUTION OF THE RADIAL EQUATION IN SPHERICAL COORDINATES—THE ENERGY EIGENVALUES THE ACCIDENTAL DEGENERACY OF THE HYDROGEN ATOM SOLUTION OF THE HYDROGEN ATOM RADIAL EQUATION IN SPHERICAL COORDINATES—THE ENERGY EIGENFUNCTIONS THE NATURE OF THE SPHERICAL EIGENFUNCTIONS SEPARATION OF THE SCHR¨ODINGER EQUATION IN PARABOLIC COORDINATES SOLUTION OF THE SEPARATED EQUATIONS IN PARABOLIC COORDINATES—THE ENERGY EIGENVALUES SOLUTION OF THE SEPARATED EQUATIONS IN PARABOLIC COORDINATES—THE ENERGY EIGENFUNCTIONS THE CLASSICAL HYDROGEN ATOM THE CLASSICAL DEGENERACY ANOTHER CONSTANT OF THE MOTION—THE LENZ VECTOR THE LENZ VECTOR AND THE ACCIDENTAL DEGENERACY THE LENZ VECTOR IN QUANTUM MECHANICS LENZ VECTOR LADDER OPERATORS; CONVERSION OF A SPHERICAL EIGENFUNCTION INTO ANOTHER SPHERICAL EIGENFUNCTION APPLICATION OF LENZ VECTOR LADDER OPERATORS TO A GENERAL SPHERICAL EIGENFUNCTION A NEW SET OF ANGULAR MOMENTUM OPERATORS ENERGY EIGENVALUES RELATIONS BETWEEN THE PARABOLIC QUANTUM NUMBERS RELATIONSHIP BETWEEN THE SPHERICAL AND PARABOLIC EIGENFUNCTIONS ADDITIONAL SYMMETRY CONSIDERATIONS BREAKING THE ACCIDENTAL DEGENERACY RELATIVISTIC CORRECTION FOR THE ELECTRONIC KINETIC ENERGY SPIN-ORBIT CORRECTION THE DARWIN TERM EVALUATION OF THE TERMS THAT CONTRIBUTE TO THE FINE-STRUCTURE OF HYDROGEN THE TOTAL FINE-STRUCTURE CORRECTION THE LAMB SHIFT HYPER?NE STRUCTURE THE SOLUTION OF THE DIRAC EQUATION THE HYDROGEN ATOM IN EXTERNAL FIELDS THE ZEEMAN EFFECT—THE HYDROGEN ATOM IN A CONSTANT MAGNETIC FIELD WEAK ELECTRIC FIELD—THE QUANTUM MECHANICAL STARK EFFECT WEAK ELECTRIC FIELD—THE CLASSICAL STARK EFFECT THE HELIUM ATOM INDISTINGUISHABLE PARTICLES THE TOTAL ENERGY OF THE HELIUM ATOM EVALUATION OF THE GROUND STATE ENERGY OF THE HELIUM ATOM USING PERTURBATION THEORY THE VARIATIONAL METHOD APPLICATION OF THE VARIATIONAL PRINCIPLE TO THE GROUND STATE OF HELIUM EXCITED STATES OF HELIUM DOUBLY EXCITED STATES OF HELIUM: AUTOIONIZATION MULTIELECTRON ATOMS ELECTRON CON?GURATION THE DESIGNATION OF STATES—LS COUPLING THE DESIGNATION OF STATES—JJ COUPLING THE QUANTUM DEFECT EVALUATION OF THE QUANTUM DEFECT CLASSICAL FORMULATION OF THE QUANTUM DEFECT AND THE CORRESPONDENCE PRINCIPLE THE CONNECTION BETWEEN THE QUANTUM DEFECT AND THE RADIAL WAVE FUNCTION MULTIELECTRON ATOMS IN EXTERNAL FIELDS THE STARK EFFECT THE ZEEMAN EFFECT INTERACTION OF ATOMS WITH RADIATION TIME DEPENDENCE OF THE WAVE FUNCTION INTERACTION OF AN ATOM WITH A SINUSOIDAL ELECTROMAGNETIC FIELD A TWO-STATE SYSTEM—THE ROTATING WAVE APPROXIMATION STIMULATED ABSORPTION AND STIMULATED EMISSION SPONTANEOUS EMISSION ANGULAR MOMENTUM SELECTION RULES SELECTION RULES FOR HYDROGEN ATOMS TRANSITIONS IN MULTIELECTRON ATOMS