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Inhaltsverzeichnis
- I The Problem: An Axiomatic Basis for Quantum Mechanics.
- 1 The Axiomatic Formulation of a Physical Theory.
- 2 The Fundamental Domain for Quantum Mechanics.
- 3 The Measurement Problem.
- II Microsystems, Preparation, and Registration Procedures.
- 1 The Concept of a Physical Object.
- 2 Selection Procedures.
- 3 Statistical Selection Procedures.
- 4 Physical Systems.
- III Ensembles and Effects.
- 1 Combinations of Preparation and Registration Methods.
- 2 Mixtures and Decompositions of Ensembles and Effects.
- 3 General Laws: Preparation and Registration of Microsystems.
- 4 Properties and Pseudoproperties.
- 5 Ensembles and Effects in Quantum Mechanics.
- 6 Decision Effects and Faces of K.
- IV Coexistent Effects and Coexistent Decompositions.
- 1 Coexistent Effects and Observables.
- 2 Structures in the Class of Observables.
- 3 Coexistent and Complementary Observables.
- 4 Realizations of Observables.
- 5 Coexistent Decompositions of Ensembles.
- 6 Complementary Decompositions of Ensembles.
- 7 Realizations of Decompositions.
- 8 Objective Properties and Pseudoproperties of Microsystems.
- V Transformations of Registration and Preparation Procedures. Transformations of Effects and Ensembles.
- 1 Morphisms for Selection Procedures.
- 2 Morphisms of Statistical Selection Procedures.
- 3 Morphisms of Preparation and Registration Procedures.
- 4 Morphisms of Ensembles and Effects.
- 5 Isomorphisms and Automorphisms of Ensembles and Effects.
- VI Representation of Groups by Means of Effect Automorphisms and Mixture Automorphisms.
- 1 Homomorphic Maps of a Group
𝒢 in the Group 𝓐 of ?-continuous Effect Automorphisms. - 2 The 𝒢-invariant Structure Corresponding to a Group Representation.
- 3 Properties of Representations of 𝒢 which are Dependent on the Special Structure of 𝓐(?) in Quantum Mechanics.
- VII The Galileo Group.
- 1 The Galileo Group as a Set of Transformations of Registration Procedures Relative to Preparation Procedures.
- 2 Irreducible Representations of the Galileo Group and Their Physical Meaning.
- 3 Irreducible Representations of the Rotation Group.
- 4 Position and Momentum Observables.
- 5 Energy and Angular Momentum Observables.
- 6 Time Observable?.
- 7 Spatial Reflections (Parity Transformations).
- 8 The Problem of the Space 𝓓 for Elementary Systems.
- 9 The Problem of Differentiability.
- VIII Composite Systems.
- 1 Registrations and Effects of the Inner Structure.
- 2 Composite Systems Consisting of Two Different Elementary Systems.
- 3 Composite Systems Consisting of Two Identical Elementary Systems.
- 4 Composite Systems Consisting of Electrons and Atomic Nuclei.
- 5 The Hamiltonian Operator.
- 6 Microsystems in External Fields.
- 7 Criticism of the Description of Interaction in Quantum Mechanics and the Problem of the Space 𝓓.
- Appendix I.
- Summary of Lattice Theory.
- 1 Definition of a Lattice.
- 2 Orthomodularity.
- 3 Boolean Rings.
- 4 Set Lattices.
- Appendix II.
- Remarks about Topological and Uniform Structures.
- 1 Topological Spaces.
- 2 Uniform Spaces.
- 3 Baire Spaces.
- 4 Connectedness.
- Appendix III.
- Banach Spaces.
- 1 Linear Vector Spaces.
- 2 Normed Vector Spaces and Banach Spaces.
- 3 The Dual Space for a Banach Space.
- 4 Weak Topologies.
- 5 Linear Maps of Banach Spaces.
- 6 Ordered Vector Spaces.
- Appendix IV.
- Operators in Hubert Space.
- 1 The Hubert Space Structure Type.
- 2 Orthogonal Systems and Closed Subspaces.
- 3 The Banach Space of Bounded Operators.
- 4 Bounded Linear Forms.
- 6 Projection Operators.
- 7 Isometric and Unitary Operators.
- 8 Spectral Representation of Self-adjoint and Unitary Operators.
- 9 The Spectrum of Compact Self-adjoint Operators.
- 10 Spectral Representation of Unbounded Self-adjoint Operators.
- 11 The Trace as a Bilinear Form.
- 12 Gleason’s Theorem.
- 13 Isomorphisms and Anti-isomorphisms.
- 14 Products of Hubert Spaces.
- References.
- List of Frequently Used Symbols.
- List of Axioms.