Now Australia's Biggest Toy Store

We won't be beaten by anyone. Guaranteed

An Axiomatic Basis for Quantum Mechanics

Product Details

Promotional Information

Springer Book Archives

Table of Contents

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 Equivalenees.- 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.

Ask a Question About this Product More...
Write your question below:
Look for similar items by category
How Fishpond Works
Fishpond works with suppliers all over the world to bring you a huge selection of products, really great prices, and delivery included on over 25 million products that we sell. We do our best every day to make Fishpond an awesome place for customers to shop and get what they want — all at the best prices online.
Webmasters, Bloggers & Website Owners
You can earn a 5% commission by selling An Axiomatic Basis for Quantum Mechanics: Volume 1 Derivation of Hilbert Space Structure on your website. It's easy to get started - we will give you example code. After you're set-up, your website can earn you money while you work, play or even sleep! You should start right now!
Authors / Publishers
Are you the Author or Publisher of a book? Or the manufacturer of one of the millions of products that we sell. You can improve sales and grow your revenue by submitting additional information on this title. The better the information we have about a product, the more we will sell!
Back to top