Foundations of Quantum Mechanics

(Volume II).- IX Representation of Hilbert Spaces by Function Spaces.- 1 Maximal Decision Observables.- 2 Representation of ? as ?2(Sp(A), ?) where Sp(A) is the Spectrum of a Scale Observable A.- 3 Improper Scalar and Vector Functions Defined on Sp(A).- 4 Transformation of One Representation into Another.- 5 Position and Momentum Representation.- 6 Degenerate Spectra.- X Equations of Motion.- 1 The Heisenberg Picture.- 2 The Schrödinger Picture.- 3 The Interaction Picture.- 4 Time Reversal Transformations.- XI The Spectrum of One-Electron Systems.- 1 The Effect of the Emission of a Photon.- 2 Ensembles Consisting of Bound States.- 3 The Spectrum of Hydrogen-like Atoms.- 4 The Eigenfunctions for the Discrete Spectrum.- 5 The Continuous Spectrum.- 6 Perturbation Theory.- 7 Perturbation Computations and Symmetry.- 8 The Spectrum of Alkali Atoms.- 9 Electron Spin.- 10 Addition of Angular Momentum.- 11 Fine Structure of Hydrogen and Alkali Metals.- XII Spectrum of Two-Electron Systems.- 1 The Hilbert Space and the Hamiltonian Operator for the Internal Motion of Atoms with n Electrons.- 2 The Spectrum of Two-Electron Atoms.- 3 Ritz Variational Principle.- 4 The Fine Structure of the Helium Spectrum.- XIII Selection Rules and the Intensity of Spectral Lines.- 1 Intensity of Spectral Lines.- 2 Representation Theory and Matrix Elements.- 3 Selection Rules for One-Electron Spectra.- 4 Selection Rules for the Helium Spectrum.- XIV Spectra of Many-Electron Systems.- 1 Energy Terms in the Absence of Spin.- 2 Fine Structure Splitting of Spectral Lines.- 3 Structure Principles.- 4 The Periodic System of the Elements.- 5 Selection and Intensity Rules.- 6 Zeeman Effect.- 7 f Electron Problems and the Symmetric Group.- 8 The Characters for the Representations of Sf and Un.- 9 Perturbation Computations.- XV Molecular Spectra and the Chemical Bond.- 1 The Hamiltonian Operator for a Molecule.- 2 The Form of the Eigenfunctions.- 3 The Ionized Hydrogen Molecule.- 4 Structure Principles for Molecular Energy Levels.- 5 Formation of a Molecule from Two Atoms.- 6 The Hydrogen Molecule.- 7 The Chemical Bond.- 8 Spectra of Diatomic Molecules.- 9 The Effect of Electron Spin on Molecular Energy Levels.- XVI Scattering Theory.- 1 General Properties of Ensembles Used in Scattering Experiments.- 2 General Properties of Effects Used in Scattering Experiments.- 3 Separation of Center of Mass Motion.- 4 Wave Operators and the Scattering Operator.- 5 Examples of Wave Operators and Scattering Operators.- 6 Examples of Registrations in Scattering Experiments.- 7 Survey of Other Problems in Scattering Theory.- XVII The Measurement Process and the Preparation Process.- 1 The Problem of Consistency.- 2 Measurement Scattering Processes.- 3 Measurement Transformations.- 4 Transpreparations.- 5 Measurements of the First Kind.- 6 The Physical Importance of Scattering Processes Used for Registration and Preparation.- 7 Complex Preparation and Registration Processes.- XVIII Quantum Mechanics, Macrophysics and Physical World Views.- 1 Universality of Quantum Mechanics?.- 2 Macroscopic Systems.- 3 Compatibility of the Measurement Process with Preparation and Registration Procedures.- 4 "Point in Time" of Measurement in Quantum Mechanics?.- 5 Relationships Between Different Theories and Quantum Mechanics.- 6 Quantum Mechanics and Cosmology.- 7 Quantum Mechanics and Physical World Views.- Appendix V Groups and Their Representations.- 1 Groups.- 2 Cosets and Invariant Subgroups.- 3 Isomorphisms and Homomorphisms.- 4 Isomorphism Theorem.- 5 Direct Products.- 6 Representations of Groups.- 7 The Irreducible Representations of a Finite Group.- 8 Orthogonality Relations for the Elements of Irreducible Representation Matrices.- 9 Representations of the Symmetric Group.- 10 Topological Groups.- References.