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Produktbild: An Axiomatic Basis for Quantum Mechanics

An Axiomatic Basis for Quantum Mechanics Volume 1 Derivation of Hilbert Space Structure

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

17.11.2011

Verlag

Springer Berlin

Seitenzahl

246

Maße (L/B/H)

24,4/17/1,5 cm

Gewicht

455 g

Auflage

Softcover reprint of the original 1st ed. 1985

Übersetzt von

L.F. Boron

Sprache

Englisch

ISBN

978-3-642-70031-6

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

17.11.2011

Verlag

Springer Berlin

Seitenzahl

246

Maße (L/B/H)

24,4/17/1,5 cm

Gewicht

455 g

Auflage

Softcover reprint of the original 1st ed. 1985

Übersetzt von

L.F. Boron

Sprache

Englisch

ISBN

978-3-642-70031-6

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: GPSR Kontakt

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  • Produktbild: An Axiomatic Basis for Quantum Mechanics
  • 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.-
    2.1 Statistical Selection Procedures.-
    2.2 Preparation Procedures.-
    2.3 Registration Procedures.-
    2.4 Dependence of Registration on Preparation.-
    3 Trajectory Preparation and Registration Procedures.-
    3.1 Trajectory Effects.-
    3.2 Trajectory Ensembles.-
    3.3 The Dynamic Laws and the Objectivating Manner of Description.-
    3.4 Dynamically Continuous Systems.-
    4 Transformations of Preparation and Registration Procedures.-
    4.1 Time Translations of the Trajectory Registration Procedures.-
    4.2 Time Translations of the Preparation Procedures.-
    4.3 Further 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.-
    5.1 The Problem of Combining Preparation and Registration Procedures.-
    5.2 Physical Systems.-
    5.3 Mixing and De-mixing of Ensembles and Effects.-
    5.4 Re-elimination of the Action Carrier.-
    6 Objectivating Method of Describing Experiments.-
    6.1 The Method of Describing Composite Macrosystems in the Trajectory Space.-
    6.2 Trajectory Effects of the Composite Systems.-
    6.3 Trajectory Ensembles of the Composite Systems.-
    6.4 The Structure of the Trajectory Measures for Directed Action.-
    6.5 Complete Description by Trajectories.-
    6.6 Use of the Interaction for the Registration of Macrosystems.-
    6.7 The Relation Between the Two Forms of an Axiomatic Basis.-
    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.-
    1.1 Coexistent Registrations.-
    1.2 Coexistent Effects.-
    1.3 Observables.-
    2 Mixture Morphisms.-
    3 Structures in the Class of Observables.-
    3.1 The Spaces ? (?) and ?’ (?) Assigned to a Boolean Ring ?.-
    3.2 Mixture Morphism Corresponding to an Observable.-
    3.3 The Kernel of an Observable.-
    3.4 De-mixing of Observables.-
    3.5 Measurement Scales of Observables and Totally Ordered Subsets of L.-
    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.-
    1.1 Increase in Sensitivity Relative to Two Effect Procedures.-
    1.2 Some Experimental and Intuitive Indications for the Law of Increase in Sensitivity.-
    1.3 Decision Effects.-
    1.4 The Increase in Sensitivity of an Effect.-
    2 Relations Between Preparation and Registration Procedures.-
    2.1 Main Law for the De-mixing of Ensembles and Related Possibilities of Registering.-
    2.2 Some Consequences of Axiom AV2.-
    3 The Lattice G.-
    4 Commensurable Decision Effects.-
    5 The Orthomodularity of G.-
    6 The Main Law for Not Coexistent Registrations.-
    6.1 Experimental Hints for Formulating the Main Law for Not Coexistent Registrations.-
    6.2 Some Important Equiválenees.-
    6.3 Formulation of the Main Law and Some Consequences.-
    7 The Main Law of Quantization.-
    7.1 Intuitive Indications for Formulating the Main Law of Quantization.-
    7.2 Simple Consequences of 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.-
    5.1 Reduction of the Elements of ?’ by the Elements of G.-
    5.2 Reduction by Center Elements.-
    5.3 Classical Systems.-
    5.4 Decomposition into Irreducible Parts.-
    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.-
    4.1 The Representation Theorem for G.-
    4.2 The Ensembles and Effects.-
    4.3 Coexistence, Commensurability, Uncertainty Relations, and Commutability of Operators.-
    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.