QUANTUM MECHANICS: A MODERN DEVELOPMENT
CONTENTS CHAPTER MATHEMATICAL PREREQUISITES 1 1 LINEAR VECTOR SPACE 1 2 LINEAR OPERATORS 1 3 SELF-ADJOINT OPERATORS 1 4 HILBERT SPACE AND RIGGED HILBERT SPACE 1 5 PROBABILITY THEORY PROBLEMS CHAPTER THE FORMULATION OF QUANTUM MECHANICS 2 1 BASIC THEORETICAL CONCEPTS 2 2 CONDITIONS ON OPERATORS 2 3 GENERAL STATES AND PURE STATES 2 4 PROBABILITY DISTRIBUTIONS KINEMATICS AND DYNAMICS 3 1 TRANSFORMATIONS OF STATES AND OBSERVABLES 3 2 THE SYMMETRIES OF SPACE–TIME 3 3 GENERATORS OF THE GALILEI GROUP 3 4 IDENTI?CATION OF OPERATORS WITH DYNAMICAL VARIABLES 3 5 COMPOSITE SYSTEMS 3 6 [[ QUANTIZING A CLASSICAL SYSTEM ]] 3 7 EQUATIONS OF MOTION 3 8 SYMMETRIES AND CONSERVATION LAWS COORDINATE REPRESENTATION AND APPLICATIONS 4 1 COORDINATE REPRESENTATION 4 2 THE WAVE EQUATION AND ITS INTERPRETATION 4 3 GALILEI TRANSFORMATION OF SCHR¨ODINGER’S EQUATION 4 4 PROBABILITY FLUX 4 5 CONDITIONS ON WAVE FUNCTIONS 4 6 ENERGY EIGENFUNCTIONS FOR FREE PARTICLES 4 7 TUNNELING 4 8 PATH INTEGRALS MOMENTUM REPRESENTATION AND APPLICATIONS 5 1 MOMENTUM REPRESENTATION 5 2 MOMENTUM DISTRIBUTION IN AN ATOM 5 3 BLOCH’S THEOREM 5 4 DI?RACTION SCATTERING: THEORY 5 5 DI?RACTION SCATTERING: EXPERIMENT 5 6 MOTION IN A UNIFORM FORCE FIELD THE HARMONIC OSCILLATOR 6 1 ALGEBRAIC SOLUTION 6 2 SOLUTION IN COORDINATE REPRESENTATION 6 3 SOLUTION IN H REPRESENTATION ANGULAR MOMENTUM 7 1 EIGENVALUES AND MATRIX ELEMENTS 7 2 EXPLICIT FORM OF THE ANGULAR MOMENTUM OPERATORS 7 3 ORBITAL ANGULAR MOMENTUM 7 4 SPIN 7 5 FINITE ROTATIONS 7 6 ROTATION THROUGH 2? 7 7 ADDITION OF ANGULAR MOMENTA 7 8 IRREDUCIBLE TENSOR OPERATORS 7 9 ROTATIONAL MOTION OF A RIGID BODY STATE PREPARATION AND DETERMINATION 8 1 STATE PREPARATION 8 2 STATE DETERMINATION 8 3 STATES OF COMPOSITE SYSTEMS 8 4 INDETERMINACY RELATIONS MEASUREMENT AND THE INTERPRETATION OF STATES 9 1 AN EXAMPLE OF SPIN MEASUREMENT 9 2 A GENERAL THEOREM OF MEASUREMENT THEORY 9 3 THE INTERPRETATION OF A STATE VECTOR 9 4 WHICH WAVE FUNCTION? 9 5 SPIN RECOMBINATION EXPERIMENT 9 6 JOINT AND CONDITIONAL PROBABILITIES CHAPTER 10 FORMATION OF BOUND STATES 10 1 SPHERICAL POTENTIAL WELL 10 2 THE HYDROGEN ATOM 10 3 ESTIMATES FROM INDETERMINACY RELATIONS 10 4 SOME UNUSUAL BOUND STATES 10 5 STATIONARY STATE PERTURBATION THEORY 10 6 VARIATIONAL METHOD CHAPTER 11 CHARGED PARTICLE IN A MAGNETIC FIELD 11 1 CLASSICAL THEORY 11 2 QUANTUM THEORY 11 3 MOTION IN A UNIFORM STATIC MAGNETIC FIELD 11 4 THE AHARONOV–BOHM E?ECT 11 5 THE ZEEMAN E?ECT CHAPTER 12 TIME-DEPENDENT PHENOMENA 12 1 SPIN DYNAMICS 12 2 EXPONENTIAL AND NONEXPONENTIAL DECAY 12 3 ENERGY–TIME INDETERMINACY RELATIONS 12 4 QUANTUM BEATS 12 5 TIME-DEPENDENT PERTURBATION THEORY 12 6 ATOMIC RADIATION 12 7 ADIABATIC APPROXIMATION CHAPTER 13 DISCRETE SYMMETRIES 13 1 SPACE INVERSION 13 2 PARITY NONCONSERVATION 13 3 TIME REVERSAL CHAPTER 14 THE CLASSICAL LIMIT 14 1 EHRENFEST’S THEOREM AND BEYOND 14 2 THE HAMILTON–JACOBI EQUATION AND THE QUANTUM POTENTIAL 14 3 QUANTAL TRAJECTORIES 14 4 THE LARGE QUANTUM NUMBER LIMIT CHAPTER 15 QUANTUM MECHANICS IN PHASE SPACE 15 1 WHY PHASE SPACE DISTRIBUTIONS? 15 2 THE WIGNER REPRESENTATION 15 3 THE HUSIMI DISTRIBUTION CHAPTER 16 SCATTERING 16 1 CROSS SECTION 16 2 SCATTERING BY A SPHERICAL POTENTIAL 16 3 GENERAL SCATTERING THEORY 16 4 BORN APPROXIMATION AND DWBA 16 5 SCATTERING OPERATORS 16 6 SCATTERING RESONANCES 16 7 DIVERSE TOPICS CHAPTER 17 IDENTICAL PARTICLES 17 1 PERMUTATION SYMMETRY 17 2 INDISTINGUISHABILITY OF PARTICLES 17 3 THE SYMMETRIZATION POSTULATE 17 4 CREATION AND ANNIHILATION OPERATORS CHAPTER 18 MANY-FERMION SYSTEMS 18 1 EXCHANGE 18 2 THE HARTREE–FOCK METHOD 18 3 DYNAMIC CORRELATIONS 18 4 FUNDAMENTAL CONSEQUENCES FOR THEORY 18 5 BCS PAIRING THEORY CHAPTER 19 QUANTUM MECHANICS OF THE ELECTROMAGNETIC FIELD 19 1 NORMAL MODES OF THE FIELD 19 2 ELECTRIC AND MAGNETIC FIELD OPERATORS 19 3 ZERO-POINT ENERGY AND THE CASIMIR FORCE 19 4 STATES OF THE EM FIELD 19 5 SPONTANEOUS EMISSION 19 6 PHOTON DETECTORS 19 7 CORRELATION FUNCTIONS 19 8 COHERENCE 19 9 OPTICAL HOMODYNE TOMOGRAPHY — DETERMINING THE QUANTUM STATE OF THE FIELD CHAPTER 20 BELL’S THEOREM AND ITS CONSEQUENCES 20 1 THE ARGUMENT OF EINSTEIN, PODOLSKY, AND ROSEN 20 2 SPIN CORRELATIONS 20 3 BELL’S INEQUALITY 20 4 A STRONGER PROOF OF BELL’S THEOREM 20 5 POLARIZATION CORRELATIONS 20 6 BELL’S THEOREM WITHOUT PROBABILITIES 20 7 IMPLICATIONS OF BELL’S THEOREM