Foundations of Quantum Mechanics I von G. Ludwig | ISBN 9783642867514

Foundations of Quantum Mechanics I

von G. Ludwig, aus dem Deutschen übersetzt von C.A. Hein
Buchcover Foundations of Quantum Mechanics I | G. Ludwig | EAN 9783642867514 | ISBN 3-642-86751-0 | ISBN 978-3-642-86751-4

Foundations of Quantum Mechanics I

von G. Ludwig, aus dem Deutschen übersetzt von C.A. Hein

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.