THE PROJECT PHYSICS COURSE: MODELS OF THE ATOM

By PAUL MARTINEZ

CONTENTS SOME NOTIONS FROM FUNCTIONAL ANALYSIS VECTOR AND NORMED SPACES METRIC AND TOPOLOGICAL SPACES COMPACTNESS TOPOLOGICAL VECTOR SPACES BANACH SPACES AND OPERATORS ON THEM THE PRINCIPLE OF UNIFORM BOUNDEDNESS SPECTRA OF CLOSED LINEAR OPERATORS NOTES TO CHAPTER 1 PROBLEMS HILBERT SPACES THE GEOMETRY OF HILBERT SPACES EXAMPLES DIRECT SUMS OF HILBERT SPACES TENSOR PRODUCTS NOTES TO CHAPTER 2 BOUNDED OPERATORS BASIC NOTIONS HERMITEAN OPERATORS UNITARY AND ISOMETRIC OPERATORS SPECTRA OF BOUNDED NORMAL OPERATORS COMPACT OPERATORS HILBERT–SCHMIDT AND TRACE–CLASS OPERATORS NOTES TO CHAPTER 3 UNBOUNDED OPERATORS THE ADJOINT CLOSED OPERATORS NORMAL OPERATORS SELF–ADJOINTNESS REDUCIBILITY UNITARY EQUIVALENCE QUADRATIC FORMS SELF–ADJOINT EXTENSIONS ORDINARY DI?ERENTIAL OPERATORS SELF–ADJOINT EXTENSIONS OF DI?ERENTIAL OPERATORS NOTES TO CHAPTER 4 SPECTRAL THEORY PROJECTION–VALUED MEASURES FUNCTIONAL CALCULUS THE SPECTRAL THEOREM SPECTRA OF SELF–ADJOINT OPERATORS FUNCTIONS OF SELF–ADJOINT OPERATORS ANALYTIC VECTORS SPECTRAL REPRESENTATION GROUPS OF UNITARY OPERATORS NOTES TO CHAPTER 5 OPERATOR SETS AND ALGEBRAS C?–ALGEBRAS GNS CONSTRUCTION W ?–ALGEBRAS NORMAL STATES ON W ?–ALGEBRAS COMMUTATIVE SYMMETRIC OPERATOR SETS COMPLETE SETS OF COMMUTING OPERATORS IRREDUCIBILITY FUNCTIONS OF NON-COMMUTING OPERATORS ALGEBRAS OF UNBOUNDED OPERATORS NOTES TO CHAPTER 6 STATES AND OBSERVABLES BASIC POSTULATES SIMPLE EXAMPLES MIXED STATES SUPERSELECTION RULES COMPATIBILITY THE ALGEBRAIC APPROACH NOTES TO CHAPTER 7 POSITION AND MOMENTUM UNCERTAINTY RELATIONS THE CANONICAL COMMUTATION RELATIONS THE CLASSICAL LIMIT AND QUANTIZATION NOTES TO CHAPTER 8 TIME EVOLUTION THE FUNDAMENTAL POSTULATE PICTURES OF MOTION TWO EXAMPLES THE FEYNMAN INTEGRAL NONCONSERVATIVE SYSTEMS UNSTABLE SYSTEMS NOTES TO CHAPTER 9 10 SYMMETRIES OF QUANTUM SYSTEMS 10 1 BASIC NOTIONS 10 2 SOME EXAMPLES 10 3 GENERAL SPACE–TIME TRANSFORMATIONS NOTES TO CHAPTER 11 COMPOSITE SYSTEMS 11 1 STATES AND OBSERVABLES 11 2 REDUCED STATES 11 3 TIME EVOLUTION 11 4 IDENTICAL PARTICLES 11 5 SEPARATION OF VARIABLES SYMMETRIES 12 THE SECOND QUANTIZATION 12 1 FOCK SPACES 12 2 CREATION AND ANNIHILATION OPERATORS 12 3 SYSTEMS OF NONINTERACTING PARTICLES 13 AXIOMATIZATION OF QUANTUM THEORY 13 1 LATTICES OF PROPOSITIONS 13 2 STATES ON PROPOSITION SYSTEMS 13 3 AXIOMS FOR QUANTUM ?ELD THEORY 14 SCHR¨ODINGER OPERATORS 14 1 SELF–ADJOINTNESS 14 2 THE MINIMAX PRINCIPLE ANALYTIC PERTURBATIONS 14 3 THE DISCRETE SPECTRUM 14 4 THE ESSENTIAL SPECTRUM 14 5 CONSTRAINED MOTION 14 6 POINT AND CONTACT INTERACTIONS 15 SCATTERING THEORY 15 1 BASIC NOTIONS 15 2 EXISTENCE OF WAVE OPERATORS 15 3 POTENTIAL SCATTERING 15 4 A MODEL OF TWO–CHANNEL SCATTERING 16 QUANTUM WAVEGUIDES 16 1 GEOMETRIC E?ECTS IN DIRICHLET STRIPES 16 2 POINT PERTURBATIONS 16 3 CURVED QUANTUM LAYERS 16 4 WEAK COUPLING 17 QUANTUM GRAPHS 17 1 ADMISSIBLE HAMILTONIANS 17 2 MEANING OF THE VERTEX COUPLING 17 3 SPECTRAL AND SCATTERING PROPERTIES 17 4 GENERALIZED GRAPHS 17 5 LEAKY GRAPHS