An Axiomatic Basis For Quantum Mechanics

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An Axiomatic Basis for Quantum Mechanics

Author : Günther Ludwig
Publisher : Springer Science & Business Media
ISBN 13 : 3642718973
Total Pages : 252 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis An Axiomatic Basis for Quantum Mechanics by : Günther Ludwig

Download or read book An Axiomatic Basis for Quantum Mechanics written by Günther Ludwig and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first volume we based quantum mechanics on the objective description of macroscopic devices. The further development of the quantum mechanics of atoms, molecules, and collision processes has been described in [2]. In this context also the usual description of composite systems by tensor products of Hilbert spaces has been introduced. This method can be formally extrapolated to systems composed of "many" ele mentary systems, even arbitrarily many. One formerly had the opinion that this "extrapolated quantum mechanics" is a more comprehensive theory than the objec tive description of macrosystems, an opinion which generated unsurmountable diffi culties for explaining the measuring process. With respect to our foundation of quan tum mechanics on macroscopic objectivity, this opinion would mean that our founda tion is no foundation at all. The task of this second volume is to attain a compatibility between the objective description of macrosystems and an extrapolated quantum mechanics. Thus in X we establish the "statistical mechanics" of macrosystems as a theory more compre hensive than an extrapolated quantum mechanics. On this basis we solve the problem of the measuring process in quantum mechan ics, in XI developing a theory which describes the measuring process as an interaction between microsystems and a macroscopic device. This theory also allows to calculate "in principle" the observable measured by a device. Neither an incorporation of consciousness nor a mysterious imagination such as "collapsing" wave packets are necessary.

An Axiomatic Basis for Quantum Mechanics

Author : G. Ludwig
Publisher : Springer Science & Business Media
ISBN 13 : 3642700292
Total Pages : 255 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis An Axiomatic Basis for Quantum Mechanics by : G. Ludwig

Download or read book An Axiomatic Basis for Quantum Mechanics written by G. Ludwig and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 detected on the basis of the macroscopic behavior of the devices. This detection resembles the detection of the dinosaurs on the basis offossils. In this first volume we develop a general description of macroscopic systems by trajectories in state spaces. This general description is a basis for the special de scription of devices consisting of two parts, where the first part is acting on the second. The microsystems are discovered as systems transmitting the action. Axioms which describe general empirical structures of the interactions between the two parts of each device, give rise to a derivation of the Hilbert space structure of quantum mechanics. Possibly, these axioms (and consequently the Hilbert space structure) may fail to describe other realms than the structure of atoms and mole cules, for instance the "elementary particles". This book supplements ref. [2]. Both together not only give an extensive foundation of quantum mechanics but also a solution in principle of the measuring problem.

Foundations of Quantum Mechanics I

Author : G. Ludwig
Publisher : Springer Science & Business Media
ISBN 13 : 3642867510
Total Pages : 437 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Foundations of Quantum Mechanics I by : G. Ludwig

Download or read book Foundations of Quantum Mechanics I written by G. Ludwig and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first volume of a two-volume work on the Foundations of Quantum Mechanics, and is intended as a new edition of the author's book Die Grundlagen der Quantenmechanik [37] which was published in 1954. In this two-volume work we will seek to obtain an improved formulation of the interpretation of quantum mechanics based on experiments. The second volume will appear shortly. Since the publication of [37] there have been several attempts to develop a basis for quantum mechanics which is, in the large part, based upon the work of J. von Neumann [38]. In particular, we mention the books ofG. W. Mackey [39], J. Jauch [40], C. Piron [41], M. Drieschner [9], and the original work ofS. P. Gudder [42], D.J. Foulis and C.H. Randall [43], and N. Zierler [44]. Here we do not seek to compare these different formulations of the foundations of quantum mechanics. We refer interested readers to [45] for such comparisons.

An Axiomatic Basis for Quantum Mechanics

Author : G. Ludwig
Publisher : Springer
ISBN 13 : 9783540137733
Total Pages : 264 pages
Book Rating : 4.1/5 (377 download)

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Book Synopsis An Axiomatic Basis for Quantum Mechanics by : G. Ludwig

Download or read book An Axiomatic Basis for Quantum Mechanics written by G. Ludwig and published by Springer. This book was released on 1985-06-01 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 detected on the basis of the macroscopic behavior of the devices. This detection resembles the detection of the dinosaurs on the basis offossils. In this first volume we develop a general description of macroscopic systems by trajectories in state spaces. This general description is a basis for the special de scription of devices consisting of two parts, where the first part is acting on the second. The microsystems are discovered as systems transmitting the action. Axioms which describe general empirical structures of the interactions between the two parts of each device, give rise to a derivation of the Hilbert space structure of quantum mechanics. Possibly, these axioms (and consequently the Hilbert space structure) may fail to describe other realms than the structure of atoms and mole cules, for instance the "elementary particles". This book supplements ref. [2]. Both together not only give an extensive foundation of quantum mechanics but also a solution in principle of the measuring problem.

An Axiomatic Basis for Quantum Mechanics

Author : Günther Ludwig
Publisher : Springer
ISBN 13 : 9783540175407
Total Pages : 264 pages
Book Rating : 4.1/5 (754 download)

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Book Synopsis An Axiomatic Basis for Quantum Mechanics by : Günther Ludwig

Download or read book An Axiomatic Basis for Quantum Mechanics written by Günther Ludwig and published by Springer. This book was released on 1987-06-26 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first volume we based quantum mechanics on the objective description of macroscopic devices. The further development of the quantum mechanics of atoms, molecules, and collision processes has been described in [2]. In this context also the usual description of composite systems by tensor products of Hilbert spaces has been introduced. This method can be formally extrapolated to systems composed of "many" ele mentary systems, even arbitrarily many. One formerly had the opinion that this "extrapolated quantum mechanics" is a more comprehensive theory than the objec tive description of macrosystems, an opinion which generated unsurmountable diffi culties for explaining the measuring process. With respect to our foundation of quan tum mechanics on macroscopic objectivity, this opinion would mean that our founda tion is no foundation at all. The task of this second volume is to attain a compatibility between the objective description of macrosystems and an extrapolated quantum mechanics. Thus in X we establish the "statistical mechanics" of macrosystems as a theory more compre hensive than an extrapolated quantum mechanics. On this basis we solve the problem of the measuring process in quantum mechan ics, in XI developing a theory which describes the measuring process as an interaction between microsystems and a macroscopic device. This theory also allows to calculate "in principle" the observable measured by a device. Neither an incorporation of consciousness nor a mysterious imagination such as "collapsing" wave packets are necessary.

Foundations and Interpretation of Quantum Mechanics

Author : Gennaro Auletta
Publisher : World Scientific
ISBN 13 : 9789810246143
Total Pages : 1030 pages
Book Rating : 4.2/5 (461 download)

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Book Synopsis Foundations and Interpretation of Quantum Mechanics by : Gennaro Auletta

Download or read book Foundations and Interpretation of Quantum Mechanics written by Gennaro Auletta and published by World Scientific. This book was released on 2001 with total page 1030 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is twofold: to provide a comprehensive account of the foundations of the theory and to outline a theoretical and philosophical interpretation suggested from the results of the last twenty years.There is a need to provide an account of the foundations of the theory because recent experience has largely confirmed the theory and offered a wealth of new discoveries and possibilities. On the other side, the following results have generated a new basis for discussing the problem of the interpretation: the new developments in measurement theory; the experimental generation of ?Schrdinger cats?; recent developments which allow, for the first time, the simultaneous measurement of complementary observables; quantum information processing, teleportation and computation.To accomplish this task, the book combines historical, systematic and thematic approaches.

Logic, Methodology and Philosophy of Science VIII

Author : J.E. Fenstad
Publisher : Elsevier
ISBN 13 : 0080879896
Total Pages : 721 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Logic, Methodology and Philosophy of Science VIII by : J.E. Fenstad

Download or read book Logic, Methodology and Philosophy of Science VIII written by J.E. Fenstad and published by Elsevier. This book was released on 1989-08-16 with total page 721 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logic, Methodology and Philosophy of Science VIII presents the results of recent research into the foundations of science. The volume contains 37 invited papers presented at the Congress, covering the areas of Logic, Mathematics, Physical Sciences, Biological Sciences and the Humanities.

Foundations of Quantum Mechanics

Author : Günther Ludwig
Publisher : Springer Science & Business Media
ISBN 13 : 3662287269
Total Pages : 431 pages
Book Rating : 4.6/5 (622 download)

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Book Synopsis Foundations of Quantum Mechanics by : Günther Ludwig

Download or read book Foundations of Quantum Mechanics written by Günther Ludwig and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this second volume on the Foundations of Quantum Mechanics we shall show how it is possible, using the methodology presented in Volume I, to deduce some of the most important applications of quantum mechanics. These deductions are concerned with the structures of the microsystems rather than the technical details of the construction of preparation and registration devices. Accordingly. the only new axioms (relative to Volume I) which are introduced are concerned with the relationship between ensemble operators W, effect operators F, and certain construction principles of the preparation and registration devices. The applications described here are concerned with the measurement of atomic and molecular structure and of collision experiments. An additional and essential step towards a theoretical description of the preparation and registration procedures is carried out in Chapter XVII. Here we demonstrate how microscopic collision processes (that is, processes which can be described by quantum mechanics) can be used to obtain novel preparation and registration procedures if we take for granted the knowledge of only a few macroscopic preparation and registration procedures. By clever use of collision processes we are often able to obtain very precise results for the operators Wand F which describe the total procedures from a very imprecise knowledge of the macroscopic parts of the preparation and regis tration processes. In this regard experimental physicists have done brilliant work. In this sense Chapter XVII represents a general theoretical foundation for the procedures used by experimental physicists.

Quantum Theory without Reduction,

Author : Cini
Publisher : Routledge
ISBN 13 : 1351420348
Total Pages : 188 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Quantum Theory without Reduction, by : Cini

Download or read book Quantum Theory without Reduction, written by Cini and published by Routledge. This book was released on 2017-10-19 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum theory offers a strange, and perhaps unique, case in the history of science. Although research into its roots has provided important results in recent years, the debate goes on. Some theorists argue that quantum theory is weakened by the inclusion of the so called "reduction of the state vector" in its foundations. Quantum Theory without Reduction presents arguments in favor of quantum theory as a consistent and complete theory without this reduction and as a theory capable of explaining all known features of the measurement problem. This collection of invited contributions defines and explores different aspects of this issue, bringing an old debate into a new perspective and leading to a more satisfying consensus about quantum theory. The book will be of interest to researchers in theoretical physics and mathematical physics involved in the foundations of quantum theory. Scientists, engineers, and philosophers interested in the conceptual problems of quantum theory will also find this work stimulating.

A New Foundation of Physical Theories

Author : Günther Ludwig
Publisher : Springer Science & Business Media
ISBN 13 : 3540308334
Total Pages : 180 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis A New Foundation of Physical Theories by : Günther Ludwig

Download or read book A New Foundation of Physical Theories written by Günther Ludwig and published by Springer Science & Business Media. This book was released on 2007-06-07 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aims to clarify and formulate the fundamental ideas of physical theories. Suitable for both physicists and philosophers of science, this book introduces the concept of idealization and reviews the process of discovering new concepts.

Quantum Theory and Pictures of Reality

Author : Wolfram Schommers
Publisher : Springer Science & Business Media
ISBN 13 : 3642955703
Total Pages : 352 pages
Book Rating : 4.6/5 (429 download)

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Book Synopsis Quantum Theory and Pictures of Reality by : Wolfram Schommers

Download or read book Quantum Theory and Pictures of Reality written by Wolfram Schommers and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Schommers introduces the foundations, mostly from a histori- cal point of view. Eberhard gives an introductory account of the Einstein-Podolsky-Rosen paradox and Bell's celebrated inequalities. D'Espagnat discusses realism andseparability and concludes that contemporary physics does not lead to a definite conception of the world. Eberhard shows how a model consistent with Bell's theorem can be constructed by ad- mitting faster-than-light action at a distance. Schommers discusses the structure ofspace-time and argues that physi- cally real processes do not take place in but are projected on space-time. Selleri discusses the idea that objectively real quantum waves exist and could in principle be detected.

Quantum Theory

Author : D. R. Bates
Publisher : Academic Press
ISBN 13 : 1483275884
Total Pages : 466 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Quantum Theory by : D. R. Bates

Download or read book Quantum Theory written by D. R. Bates and published by Academic Press. This book was released on 2013-10-22 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Theory: A Treatise in Three Volumes, I: Elements focuses on the principles, methodologies, and approaches involved in quantum theory, including quantum mechanics, linear combinations, collisions, and transitions. The selection first elaborates on the fundamental principles of quantum mechanics, exactly soluble bound state problems, and continuum. Discussions focus on delta function normalization, spherically symmetric potentials, rectangular potential wells, harmonic oscillators, spherically symmetrical potentials, Coulomb potential, axiomatic basis, consequences of first three postulates, and time-dependent states. The text then examines the stationary perturbation theory, variational method, and the asymptotic approximation method. Concerns cover the application of the asymptotic approximation method to potential barrier problems, method of linear combinations, lower bounds for the ground state eigenenergy, relative degeneracy, and degenerate case. The publication examines the theory of collisions and transitions, including the scattering of identical particles, Coulomb field, methods of determining scattering phases, persistent perturbations, and adiabatic approximation. The selection is a valuable source of information for researchers interested in quantum theory.

Measuring the Quantum State of Light

Author : Ulf Leonhardt
Publisher : Cambridge University Press
ISBN 13 : 9780521497305
Total Pages : 236 pages
Book Rating : 4.4/5 (973 download)

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Book Synopsis Measuring the Quantum State of Light by : Ulf Leonhardt

Download or read book Measuring the Quantum State of Light written by Ulf Leonhardt and published by Cambridge University Press. This book was released on 1997-07-13 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Appendix A: Semiclassical approximation

Mathematical Foundations of Quantum Mechanics

Author : John von Neumann
Publisher : Princeton University Press
ISBN 13 : 9780691028934
Total Pages : 462 pages
Book Rating : 4.0/5 (289 download)

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Book Synopsis Mathematical Foundations of Quantum Mechanics by : John von Neumann

Download or read book Mathematical Foundations of Quantum Mechanics written by John von Neumann and published by Princeton University Press. This book was released on 1955 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: A revolutionary book that for the first time provided a rigorous mathematical framework for quantum mechanics. -- Google books

The Wave Function

Author : Alyssa Ney
Publisher : Oxford University Press
ISBN 13 : 019979054X
Total Pages : 244 pages
Book Rating : 4.1/5 (997 download)

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Book Synopsis The Wave Function by : Alyssa Ney

Download or read book The Wave Function written by Alyssa Ney and published by Oxford University Press. This book was released on 2013-03-28 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a new volume of original essays on the metaphysics of quantum mechanics. The essays address questions such as: What fundamental metaphysics is best motivated by quantum mechanics? What is the ontological status of the wave function? What is the nature of the fundamental space (or space-time manifold) of quantum mechanics?

Quantum Theory: Informational Foundations and Foils

Author : Giulio Chiribella
Publisher : Springer
ISBN 13 : 9401773033
Total Pages : 525 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Quantum Theory: Informational Foundations and Foils by : Giulio Chiribella

Download or read book Quantum Theory: Informational Foundations and Foils written by Giulio Chiribella and published by Springer. This book was released on 2015-12-08 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first unified overview of the burgeoning research area at the interface between Quantum Foundations and Quantum Information. Topics include: operational alternatives to quantum theory, information-theoretic reconstructions of the quantum formalism, mathematical frameworks for operational theories, and device-independent features of the set of quantum correlations. Powered by the injection of fresh ideas from the field of Quantum Information and Computation, the foundations of Quantum Mechanics are in the midst of a renaissance. The last two decades have seen an explosion of new results and research directions, attracting broad interest in the scientific community. The variety and number of different approaches, however, makes it challenging for a newcomer to obtain a big picture of the field and of its high-level goals. Here, fourteen original contributions from leading experts in the field cover some of the most promising research directions that have emerged in the new wave of quantum foundations. The book is directed at researchers in physics, computer science, and mathematics and would be appropriate as the basis of a graduate course in Quantum Foundations.

Probability And Schrodinger's Mechanics

Author : David B Cook
Publisher : World Scientific
ISBN 13 : 9814487279
Total Pages : 343 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Probability And Schrodinger's Mechanics by : David B Cook

Download or read book Probability And Schrodinger's Mechanics written by David B Cook and published by World Scientific. This book was released on 2002-12-26 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses some of the problems of interpreting Schrödinger's mechanics — the most complete and explicit theory falling under the umbrella of “quantum theory”. The outlook is materialist (“realist”) and stresses the development of Schrödinger's mechanics from classical theories and its close connections with (particularly) the Hamilton-Jacobi theory. Emphasis is placed on the concepts and use of the modern objective (measure-theoretic) probability theory. The work is free from any mention of the bearing of Schrödinger's mechanics on God, his alleged mind or, indeed, minds at all. The author has taken the naïve view that this mechanics is about the structure and dynamics of atomic and sub-atomic systems since he has been unable to trace any references to minds, consciousness or measurements in the foundations of the theory.