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Author: Paul Busch
Publisher: Springer
ISBN: 331943389X
Category : Science
Languages : en
Pages : 544
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Book Description
This is a book about the Hilbert space formulation of quantum mechanics and its measurement theory. It contains a synopsis of what became of the Mathematical Foundations of Quantum Mechanics since von Neumann’s classic treatise with this title. Fundamental non-classical features of quantum mechanics—indeterminacy and incompatibility of observables, unavoidable measurement disturbance, entanglement, nonlocality—are explicated and analysed using the tools of operational quantum theory. The book is divided into four parts: 1. Mathematics provides a systematic exposition of the Hilbert space and operator theoretic tools and relevant measure and integration theory leading to the Naimark and Stinespring dilation theorems; 2. Elements develops the basic concepts of quantum mechanics and measurement theory with a focus on the notion of approximate joint measurability; 3. Realisations offers in-depth studies of the fundamental observables of quantum mechanics and some of their measurement implementations; and 4. Foundations discusses a selection of foundational topics (quantum-classical contrast, Bell nonlocality, measurement limitations, measurement problem, operational axioms) from a measurement theoretic perspective. The book is addressed to physicists, mathematicians and philosophers of physics with an interest in the mathematical and conceptual foundations of quantum physics, specifically from the perspective of measurement theory.
Author: Paul Busch
Publisher: Springer
ISBN: 331943389X
Category : Science
Languages : en
Pages : 544
Get Book Here
Book Description
This is a book about the Hilbert space formulation of quantum mechanics and its measurement theory. It contains a synopsis of what became of the Mathematical Foundations of Quantum Mechanics since von Neumann’s classic treatise with this title. Fundamental non-classical features of quantum mechanics—indeterminacy and incompatibility of observables, unavoidable measurement disturbance, entanglement, nonlocality—are explicated and analysed using the tools of operational quantum theory. The book is divided into four parts: 1. Mathematics provides a systematic exposition of the Hilbert space and operator theoretic tools and relevant measure and integration theory leading to the Naimark and Stinespring dilation theorems; 2. Elements develops the basic concepts of quantum mechanics and measurement theory with a focus on the notion of approximate joint measurability; 3. Realisations offers in-depth studies of the fundamental observables of quantum mechanics and some of their measurement implementations; and 4. Foundations discusses a selection of foundational topics (quantum-classical contrast, Bell nonlocality, measurement limitations, measurement problem, operational axioms) from a measurement theoretic perspective. The book is addressed to physicists, mathematicians and philosophers of physics with an interest in the mathematical and conceptual foundations of quantum physics, specifically from the perspective of measurement theory.
Author: G. Kalmbach
Publisher: Springer
ISBN: 9789401728294
Category : Mathematics
Languages : en
Pages : 0
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Book Description
This book has evolved from lectures and seminars of the author, held at different academic institutions during the years 1983-1998. It has four parts. In the first part orthomodular measure theory, generalizing classical measure theory for the purpose of quantum mechanics, is developed. Quantum structures are investigated and inner products are constructed in rich supply for measurements. This part has grown out of Hilbert space and operator theory and the quantum mechanical measurement process. In the second part a new finite-dimensional geometrical model is presented for the four basic interactions, for bags and particle series. Symmetry transfor mation groups, such as U(1), SU(2), SU(3), together with a new group D , are 3 here the guides for the geometric constructions. Infinite dimensional spaces are the theme of the third part of the book: Hilbert lattices are special dimension lattices. Complete spaces, archimedean and non-archimedean orthomodular spaces are studied or characterized, and coordinates and dimension functions for such spaces are constructed. In the last part of the book, brief reviews are found on topics, diversely spread in the literature. They are intended as reference for an interested reader, which want to know some more details, concerning the material of this book. The book can be used for future research, for seminars and lectures on quantum structures. It is a continuation of the author's book on orthomodular lattices.
Author: Howard M. Wiseman
Publisher: Cambridge University Press
ISBN: 0521804426
Category : Mathematics
Languages : en
Pages : 477
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Book Description
Modern quantum measurement for graduate students and researchers in quantum information, quantum metrology, quantum control and related fields.
Author: Gudrun Kalmbach
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 366
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Book Description
This book has evolved from lectures and seminars of the author, held at different academic institutions during the years 1983-1998. It has four parts. In the first part orthomodular measure theory, generalizing classical measure theory for the purpose of quantum mechanics, is developed. Quantum structures are investigated and inner products are constructed in rich supply for measurements. This part has grown out of Hilbert space and operator theory and the quantum mechanical measurement process. In the second part a new finite-dimensional geometrical model is presented for the four basic interactions, for bags and particle series. Symmetry transfor mation groups, such as U(1), SU(2), SU(3), together with a new group D , are 3 here the guides for the geometric constructions. Infinite dimensional spaces are the theme of the third part of the book: Hilbert lattices are special dimension lattices. Complete spaces, archimedean and non-archimedean orthomodular spaces are studied or characterized, and coordinates and dimension functions for such spaces are constructed. In the last part of the book, brief reviews are found on topics, diversely spread in the literature. They are intended as reference for an interested reader, which want to know some more details, concerning the material of this book. The book can be used for future research, for seminars and lectures on quantum structures. It is a continuation of the author's book on orthomodular lattices.
Author: Paul Busch
Publisher: Springer Science & Business Media
ISBN: 3540613552
Category : Science
Languages : en
Pages : 193
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Book Description
The amazing accuracy in verifying quantum effects experimentally has recently renewed interest in quantum mechanical measurement theory. In this book the authors give within the Hilbert space formulation of quantum mechanics a systematic exposition of the quantum theory of measurement. Their approach includes the concepts of unsharp objectification and of nonunitary transformations needed for a unifying description of various detailed investigations. The book addresses advanced students and researchers in physics and philosophy of science. In this second edition Chaps. II-IV have been substantially rewritten. In particular, an insolubility theorem for the objectification problem has been formulated in full generality, which includes unsharp object observables as well as unsharp pointers.
Author: Michael J. W. Hall
Publisher: Springer
ISBN: 3319341669
Category : Science
Languages : en
Pages : 284
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Book Description
This book describes a promising approach to problems in the foundations of quantum mechanics, including the measurement problem. The dynamics of ensembles on configuration space is shown here to be a valuable tool for unifying the formalisms of classical and quantum mechanics, for deriving and extending the latter in various ways, and for addressing the quantum measurement problem. A description of physical systems by means of ensembles on configuration space can be introduced at a very fundamental level: the basic building blocks are a configuration space, probabilities, and Hamiltonian equations of motion for the probabilities. The formalism can describe both classical and quantum systems, and their thermodynamics, with the main difference being the choice of ensemble Hamiltonian. Furthermore, there is a natural way of introducing ensemble Hamiltonians that describe the evolution of hybrid systems; i.e., interacting systems that have distinct classical and quantum sectors, allowing for consistent descriptions of quantum systems interacting with classical measurement devices and quantum matter fields interacting gravitationally with a classical spacetime.
Author: David W. Cohen
Publisher: Springer Science & Business Media
ISBN: 1461388414
Category : Science
Languages : en
Pages : 159
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Book Description
Historically, nonclassical physics developed in three stages. First came a collection of ad hoc assumptions and then a cookbook of equations known as "quantum mechanics". The equations and their philosophical underpinnings were then collected into a model based on the mathematics of Hilbert space. From the Hilbert space model came the abstaction of "quantum logics". This book explores all three stages, but not in historical order. Instead, in an effort to illustrate how physics and abstract mathematics influence each other we hop back and forth between a purely mathematical development of Hilbert space, and a physically motivated definition of a logic, partially linking the two throughout, and then bringing them together at the deepest level in the last two chapters. This book should be accessible to undergraduate and beginning graduate students in both mathematics and physics. The only strict prerequisites are calculus and linear algebra, but the level of mathematical sophistication assumes at least one or two intermediate courses, for example in mathematical analysis or advanced calculus. No background in physics is assumed.
Author: Shan Gao
Publisher: Cambridge University Press
ISBN: 1107069637
Category : Psychology
Languages : en
Pages : 251
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Book Description
With contributions from two of the original discoverers of protective measurement, this book investigates its broad applications and deep implications. Addressing both physical and philosophical aspects, this is a valuable resource for graduate students and researchers interested in the conceptual foundations of quantum mechanics.
Author: John Archibald Wheeler
Publisher: Princeton University Press
ISBN: 1400854555
Category : Science
Languages : en
Pages : 841
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Book Description
The forty-nine papers collected here illuminate the meaning of quantum theory as it is disclosed in the measurement process. Together with an introduction and a supplemental annotated bibliography, they discuss issues that make quantum theory, overarching principle of twentieth-century physics, appear to many to prefigure a new revolution in science. Originally published in 1983. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author: Richard H. Hellman
Publisher: U of Minnesota Press
ISBN: 9781452903354
Category :
Languages : en
Pages : 226
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Book Description
