An Axiomatic Basis For Quantum Mechanics
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An Axiomatic Basis For Quantum Mechanics Derivation Of Hilbert Space Structure
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Author : Günther Ludwig
language : en
Publisher: Springer
Release Date : 1985
An Axiomatic Basis For Quantum Mechanics Derivation Of Hilbert Space Structure 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 Mathematics 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 : Günther Ludwig
language : en
Publisher: Springer
Release Date : 1987-06-26
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 1987-06-26 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.
An Axiomatic Basis For Quantum Mechanics
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Author : Günther Ludwig
language : en
Publisher:
Release Date : 1987
An Axiomatic Basis For Quantum Mechanics written by Günther Ludwig and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Axioms categories.
Introduction To Quantum Mechanics
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Author : Bernardo Adeva Andany
language : en
Publisher: Bernardo Adeva
Release Date : 2015-09-08
Introduction To Quantum Mechanics written by Bernardo Adeva Andany and has been published by Bernardo Adeva this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-08 with Science categories.
This course contains a brief and mathematically precise introduction to the conceptual body, and calculation tools, of Quantum Mechanics and Quantum Physics. It is addressed to undergraduate students. The introduction is performed using the semiclassical framework, where Newton´s Classical Mechanics and Relativity as the reference points. Feynman's propagation is used as an axiomatic basis for Quantum Mechanics, completed with the generally admitted ideas about the measurement problem. As a book, it has been revised and re-edited in 2016, 2018 and 2022, and it is now available from Amazon KDP in paperback and as a Kindle Book (see https://www.amazon.com/dp/B09V3X4YK1 in US).
Quantum Mechanics
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Author : Nelson Bolivar
language : en
Publisher: CRC Press
Release Date : 2018-05-23
Quantum Mechanics written by Nelson Bolivar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-23 with Science categories.
This volume will act as a guide through the various aspects of quantum mechanics. It not only covers the basics but also addresses new themes developed in the field of quantum mechanics in recent years. These include quantum mechanics in relation to electronics, quantum dots, spintronics, cryptography, and other more theoretical aspects, such as the path integral formulation and supersymmetric quantum mechanics. The volume presents a number of mathematical tools and physical consequences derived from quantum mechanics. The starting point of the volume is a very brief review of the phenomenology associated with the origins of quantum theory, as the branch of science was understood in the beginning of the 20th century, leading to an interpretation of the results at that time. Key features: • Provides understanding and demystification of the quantum theory • Presents applications to information theory and encryption • Introduces applications to medicine, in both treatment and diagnosis • Covers applications to modern communications systems • Looks at the philosophical implications of quantum mechanics, its reality, and its perception • Describes the application to the basics of solid state devices
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.
Quantum Mathematical Physics
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Author : Walter Thirring
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
Quantum Mathematical Physics written by Walter Thirring 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 2013-04-18 with Science categories.
This book is a new edition of Volumes 3 and 4 of Walter Thirring’s famous textbook on mathematical physics. The first part is devoted to quantum mechanics and especially to its applications to scattering theory, atoms and molecules. The second part deals with quantum statistical mechanics examining fundamental concepts like entropy, ergodicity and thermodynamic functions.
Intuition And The Axiomatic Method
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Author : Emily Carson
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-24
Intuition And The Axiomatic Method written by Emily Carson 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 2006-01-24 with Mathematics categories.
Following developments in modern geometry, logic and physics, many scientists and philosophers in the modern era considered Kant’s theory of intuition to be obsolete. But this only represents one side of the story concerning Kant, intuition and twentieth century science. Several prominent mathematicians and physicists were convinced that the formal tools of modern logic, set theory and the axiomatic method are not sufficient for providing mathematics and physics with satisfactory foundations. All of Hilbert, Gödel, Poincaré, Weyl and Bohr thought that intuition was an indispensable element in describing the foundations of science. They had very different reasons for thinking this, and they had very different accounts of what they called intuition. But they had in common that their views of mathematics and physics were significantly influenced by their readings of Kant. In the present volume, various views of intuition and the axiomatic method are explored, beginning with Kant’s own approach. By way of these investigations, we hope to understand better the rationale behind Kant’s theory of intuition, as well as to grasp many facets of the relations between theories of intuition and the axiomatic method, dealing with both their strengths and limitations; in short, the volume covers logical and non-logical, historical and systematic issues in both mathematics and physics.