An Axiomatic Basis For Quantum Mechanics
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An Axiomatic Basis For Quantum Mechanics
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Author : G. Ludwig
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
An Axiomatic Basis For Quantum Mechanics written by G. Ludwig and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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
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Author : Günther Ludwig
language : en
Publisher: Springer
Release Date : 1985
An Axiomatic Basis For Quantum Mechanics written by Günther Ludwig and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Science categories.
An Axiomatic Basis For Quantum Mechanics
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Author : Günther Ludwig
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
An Axiomatic Basis For Quantum Mechanics written by Günther Ludwig and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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
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Author : G. Ludwig
language : en
Publisher: Springer
Release Date : 2011-11-17
An Axiomatic Basis For Quantum Mechanics written by G. Ludwig and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-17 with Science categories.
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.
Quantum Theory Without Reduction
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Author : Cini
language : en
Publisher: CRC Press
Release Date : 1990-01-01
Quantum Theory Without Reduction written by Cini and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Science categories.
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.
Foundations Of Quantum Mechanics I
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Author : G. Ludwig
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Foundations Of Quantum Mechanics I written by G. Ludwig and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
A New Foundation Of Physical Theories
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Author : Günther Ludwig
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-11
A New Foundation Of Physical Theories written by Günther Ludwig and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-11 with Science categories.
Written in the tradition of G. Ludwig’s groundbreaking works, this book aims to clarify and formulate more precisely the fundamental ideas of physical theories. By introducing a basic descriptive language of simple form, in which it is possible to formulate recorded facts, ambiguities of physical theories are avoided as much as possible. In this approach the field of physics that should be described by a theory is determined by basic concepts only, i.e. concepts that can be explained without a theory. In this context the authors introduce a new concept of idealization and review the process of discovering new concepts. They believe that, when the theories are formulated within an axiomatic basis, solutions can be found to many difficult problems such as the interpretation of physical theories, the relations between theories as well as the introduction of physical concepts. The book addresses both physicists and philosophers of science and should encourage the reader to contribute to the understanding of the lasting core of physical knowledge about the real structures of the world.
Probability And Schrodinger S Mechanics
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Author : David B Cook
language : en
Publisher: World Scientific
Release Date : 2002-12-26
Probability And Schrodinger S Mechanics written by David B Cook and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-26 with Science categories.
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.
Quantum Theory
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Author : D. R. Bates
language : en
Publisher: Academic Press
Release Date : 2013-10-22
Quantum Theory written by D. R. Bates and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Science categories.
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.
Algorithms And Complexity In Mathematics Epistemology And Science
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Author : Nicolas Fillion
language : en
Publisher: Springer
Release Date : 2019-02-07
Algorithms And Complexity In Mathematics Epistemology And Science written by Nicolas Fillion and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-07 with Mathematics categories.
ACMES (Algorithms and Complexity in Mathematics, Epistemology, and Science) is a multidisciplinary conference series that focuses on epistemological and mathematical issues relating to computation in modern science. This volume includes a selection of papers presented at the 2015 and 2016 conferences held at Western University that provide an interdisciplinary outlook on modern applied mathematics that draws from theory and practice, and situates it in proper context. These papers come from leading mathematicians, computational scientists, and philosophers of science, and cover a broad collection of mathematical and philosophical topics, including numerical analysis and its underlying philosophy, computer algebra, reliability and uncertainty quantification, computation and complexity theory, combinatorics, error analysis, perturbation theory, experimental mathematics, scientific epistemology, and foundations of mathematics. By bringing together contributions from researchers who approach the mathematical sciences from different perspectives, the volume will further readers' understanding of the multifaceted role of mathematics in modern science, informed by the state of the art in mathematics, scientific computing, and current modeling techniques.