QUANTUM MECHANICS

By PAUL TAYLOR

CONTENTS LAGRANGIAN MECHANICS BASICS OF VARIATIONAL CALCULUS SYMMETRY PROPERTIES IN LAGRANGIAN MECHANICS QUANTUM MECHANICAL PATH INTEGRAL THE DOUBLE SLIT EXPERIMENT AXIOMS FOR QUANTUM MECHANICAL DESCRIPTION OF SINGLE PARTICLE HOW TO EVALUATE THE PATH INTEGRAL PROPAGATOR FOR A FREE PARTICLE PROPAGATOR FOR A QUADRATIC LAGRANGIAN WAVE PACKET MOVING IN HOMOGENEOUS FORCE FIELD STATIONARY STATES OF THE HARMONIC OSCILLATOR THE SCHR¨ODINGER EQUATION DERIVATION OF THE SCHR¨ODINGER EQUATION BOUNDARY CONDITIONS PARTICLE FLUX AND SCHR¨ODINGER EQUATION SOLUTION OF THE FREE PARTICLE SCHR¨ODINGER EQUATION PARTICLE IN ONE-DIMENSIONAL BOX PARTICLE IN THREE-DIMENSIONAL BOX LINEAR HARMONIC OSCILLATOR CREATION AND ANNIHILATION OPERATORS GROUND STATE OF THE HARMONIC OSCILLATOR EXCITED STATES OF THE HARMONIC OSCILLATOR PROPAGATOR FOR THE HARMONIC OSCILLATOR WORKING WITH LADDER OPERATORS MOMENTUM REPRESENTATION FOR THE HARMONIC OSCILLATOR QUASI-CLASSICAL STATES OF THE HARMONIC OSCILLATOR THEORY OF ANGULAR MOMENTUM AND SPIN MATRIX REPRESENTATION OF THE GROUP SO(3) FUNCTION SPACE REPRESENTATION OF THE GROUP SO(3) ANGULAR MOMENTUM OPERATORS ANGULAR MOMENTUM EIGENSTATES IRREDUCIBLE REPRESENTATIONS WIGNER ROTATION MATRICES SPIN 2 AND THE GROUP SU(2) GENERATORS AND ROTATION MATRICES OF SU(2) CONSTRUCTING SPIN STATES WITH LARGER QUANTUM NUMBERS THROUGH SPINOR OPERATORS 5 10 ALGEBRAIC PROPERTIES OF SPINOR OPERATORS 5 11 EVALUATION OF THE ELEMENTS DJ M M?(?) OF THE WIGNER ROTATION MATRIX 5 12 MAPPING OF SU(2) ONTO SO(3) QUANTUM MECHANICAL ADDITION OF ANGULAR MOMENTA AND SPIN CLEBSCH-GORDAN COE?CIENTS CONSTRUCTION OF CLEBSCH-GORDAN COE?CIENTS EXPLICIT EXPRESSION FOR THE CLEBSCH–GORDAN COE?CIENTS SYMMETRIES OF THE CLEBSCH-GORDAN COE?CIENTS EXAMPLE: SPIN–ORBITAL ANGULAR MOMENTUM STATES THE 3J–COE?CIENTS TENSOR OPERATORS AND WIGNER-ECKART THEOREM WIGNER-ECKART THEOREM MOTION IN SPHERICALLY SYMMETRIC POTENTIALS RADIAL SCHR¨ODINGER EQUATION FREE PARTICLE DESCRIBED IN SPHERICAL COORDINATES INTERACTION OF CHARGED PARTICLES WITH ELECTROMAGNETIC RADIATION DESCRIPTION OF THE CLASSICAL ELECTROMAGNETIC FIELD / SEPARATION OF LONGITUDINAL AND TRANSVERSE COMPONENTS PLANAR ELECTROMAGNETIC WAVES HAMILTON OPERATOR ELECTRON IN A STATIONARY HOMOGENEOUS MAGNETIC FIELD TIME-DEPENDENT PERTURBATION THEORY PERTURBATIONS DUE TO ELECTROMAGNETIC RADIATION ONE-PHOTON ABSORPTION AND EMISSION IN ATOMS TWO-PHOTON PROCESSES MANY–PARTICLE SYSTEMS PERMUTATION SYMMETRY OF BOSONS AND FERMIONS OPERATORS OF 2ND QUANTIZATION ONE– AND TWO–PARTICLE OPERATORS INDEPENDENT-PARTICLE MODELS SELF-CONSISTENT FIELD THEORY SELF-CONSISTENT FIELD ALGORITHM PROPERTIES OF THE SCF GROUND STATE MEAN FIELD THEORY FOR MACROSCOPIC SYSTEMS CONTENTS 10 RELATIVISTIC QUANTUM MECHANICS 10 1 NATURAL REPRESENTATION OF THE LORENTZ GROUP 10 2 SCALARS, 4–VECTORS AND TENSORS 10 3 RELATIVISTIC ELECTRODYNAMICS 10 4 FUNCTION SPACE REPRESENTATION OF LORENTZ GROUP 10 5 KLEIN–GORDON EQUATION 10 6 KLEIN–GORDON EQUATION FOR PARTICLES IN AN ELECTROMAGNETIC FIELD 10 7 THE DIRAC EQUATION 10 8 LORENTZ INVARIANCE OF THE DIRAC EQUATION 10 9 SOLUTIONS OF THE FREE PARTICLE DIRAC EQUATION 10 10DIRAC PARTICLES IN ELECTROMAGNETIC FIELD 11 SPINOR FORMULATION OF RELATIVISTIC QUANTUM MECHANICS 11 1 THE LORENTZ TRANSFORMATION OF THE DIRAC BISPINOR 11 2 RELATIONSHIP BETWEEN THE LIE GROUPS SL(2,C) AND SO(3,1) 11 3 SPINORS 11 4 SPINOR TENSORS 11 5 LORENTZ INVARIANT FIELD EQUATIONS IN SPINOR FORM 12 SYMMETRIES IN PHYSICS: ISOSPIN AND THE EIGHTFOLD WAY 12 1 SYMMETRY AND DEGENERACIES 12 2 ISOSPIN AND THE SU(2) ?AVOR SYMMETRY 12 3 THE EIGHTFOLD WAY AND THE ?AVOR SU(3) SYMMETRY