An Axiomatic Basis for Quantum Mechanics [E-Book] : Volume 1 Derivation of Hilbert Space Structure / by Günther Ludwig.
This book is the first volume of a two-volume work, which is an improved version of a preprint [47] published in German. We seek to deduce the funda mental concepts of quantum mechanics solely from a description of macroscopic devices. The microscopic systems such as electrons, atoms, etc. must be...
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Full text |
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Personal Name(s): | Ludwig, Günther, author |
Imprint: |
Berlin, Heidelberg :
Springer,
1985
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Physical Description: |
X, 246 p. online resource. |
Note: |
englisch |
ISBN: |
9783642700293 |
DOI: |
10.1007/978-3-642-70029-3 |
Subject (LOC): |
- I The Problem of Formulating an Axiomatics for Quantum Mechanics
- § 1 Is There an Axiomatic Basis for Quantum Mechanics?
- § 2 Concepts Unsuitable in a Basis for Quantum Mechanics
- § 3 Experimental Situations Describable Solely by Pretheories
- § 4 Mathematical Problems
- § 5 Progress to More Comprehensive Theories
- II Pretheories for Quantum Mechanics
- § 1 State Space and Trajectory Space
- § 2 Preparation and Registration Procedures
- § 3 Trajectory Preparation and Registration Procedures
- § 4 Transformations of Preparation and Registration Procedures
- § 5 The Macrosystems as Physical Objects
- III Base Sets and Fundamental Structure Terms for a Theory of Microsystems
- § 1 Composite Macrosystems
- § 2 Preparation and Registration Procedures for Composite Macrosystems
- § 3 Directed Interactions
- § 4 Action Carriers
- § 5 Ensembles and Effects
- § 6 Objectivating Method of Describing Experiments
- § 7 Transport of Systems Relative to Each Other
- IV Embedding of Ensembles and Effect Sets in Topological Vector Spaces
- § 1 Embedding of K, L in a Dual Pair of Vector Spaces
- § 2 Uniform Structures of the Physical Imprecision on K and L
- § 3 Embedding of K and L in Topologically Complete Vector Spaces
- § 4 ?, ?’, D, D’ Considered as Ordered Vector Spaces
- § 5 The Faces of K and L
- § 6 Some Convergence Theorems
- V Observables and Preparators
- § 1 Coexistent Effects and Observables
- § 4 Coexistent and Complementary Observables
- § 5 Realization of Observables
- § 6 Coexistent De-mixing of Ensembles
- § 7 Complementary De-mixings of Ensembles
- § 8 Realizations of De-mixings
- § 9 Preparators and Faces of K
- § 10 Physical Objects as Action Carriers
- § 11 Operations and Transpreparators
- VI Main Laws of Preparation and Registration
- § 1 Main Laws for the Increase in Sensitivity of Registrations
- § 2 Relations Between Preparation and Registration Procedures
- § 3 The Lattice G
- § 4 Commensurable Decision Effects
- § 5 The Orthomodularity of G
- § 6 The Main Law for Not Coexistent Registrations
- § 7 The Main Law of Quantization
- VII Decision Observables and the Center
- § 1 The Commutator of a Set of Decision Effects
- § 2 Decision Observables
- § 3 Structures in That Class of Observables Whose Range also Contains Elements of G
- § 4 Commensurable Decision Observables
- § 5 Decomposition of ? and ?’ Relative to the Center Z
- § 6 System Types and Super Selection Rules
- VIII Representation of ?, ?’ by Banach Spaces of Operators in a Hilbert Space
- § 1 The Finite Elements of G
- § 2 The General Representation Theorem for Irreducible G
- § 3 Some Topological Properties of G
- § 4 The Representation Theorem for K, L
- § 5 Some Theorems for Finite-dimensional and Irreducible ?
- A II Banach Lattices
- A III The Axiom AVid and the Minimal Decomposition Property
- A IV The Bishop-Phelps Theorem and the Ellis Theorem
- List of Frequently Used Symbols
- List of Axioms.