An Introduction to Hilbert Space and Quantum Logic

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Publisher : Springer Science & Business Media
ISBN 13 : 1461388414
Total Pages : 159 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis An Introduction to Hilbert Space and Quantum Logic by : David W. Cohen

Download or read book An Introduction to Hilbert Space and Quantum Logic written by David W. Cohen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum Mechanics

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Publisher : Springer Science & Business Media
ISBN 13 : 9401153329
Total Pages : 247 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum Mechanics by : W.-H. Steeb

Download or read book Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum Mechanics written by W.-H. Steeb and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive introduction to modern quantum mechanics, emphasising the underlying Hilbert space theory and generalised function theory. All the major modern techniques and approaches used in quantum mechanics are introduced, such as Berry phase, coherent and squeezed states, quantum computing, solitons and quantum mechanics. Audience: The book is suitable for graduate students in physics and mathematics.

Categories for Quantum Theory

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Publisher : Oxford University Press
ISBN 13 : 0191060062
Total Pages : 320 pages
Book Rating : 4.1/5 (91 download)

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Book Synopsis Categories for Quantum Theory by : Chris Heunen

Download or read book Categories for Quantum Theory written by Chris Heunen and published by Oxford University Press. This book was released on 2019-11-14 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monoidal category theory serves as a powerful framework for describing logical aspects of quantum theory, giving an abstract language for parallel and sequential composition, and a conceptual way to understand many high-level quantum phenomena. This text lays the foundation for this categorical quantum mechanics, with an emphasis on the graphical calculus which makes computation intuitive. Biproducts and dual objects are introduced and used to model superposition and entanglement, with quantum teleportation studied abstractly using these structures. Monoids, Frobenius structures and Hopf algebras are described, and it is shown how they can be used to model classical information and complementary observables. The CP construction, a categorical tool to describe probabilistic quantum systems, is also investigated. The last chapter introduces higher categories, surface diagrams and 2-Hilbert spaces, and shows how the language of duality in monoidal 2-categories can be used to reason about quantum protocols, including quantum teleportation and dense coding. Prior knowledge of linear algebra, quantum information or category theory would give an ideal background for studying this text, but it is not assumed, with essential background material given in a self-contained introductory chapter. Throughout the text links with many other areas are highlighted, such as representation theory, topology, quantum algebra, knot theory, and probability theory, and nonstandard models are presented, such as sets and relations. All results are stated rigorously, and full proofs are given as far as possible, making this book an invaluable reference for modern techniques in quantum logic, with much of the material not available in any other textbook.

Hilbert Space And Quantum Mechanics

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Author :
Publisher : World Scientific Publishing Company
ISBN 13 : 9814635855
Total Pages : 761 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Hilbert Space And Quantum Mechanics by : Franco Gallone

Download or read book Hilbert Space And Quantum Mechanics written by Franco Gallone and published by World Scientific Publishing Company. This book was released on 2014-12-23 with total page 761 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topics of this book are the mathematical foundations of non-relativistic quantum mechanics and the mathematical theory they require. The main characteristic of the book is that the mathematics is developed assuming familiarity with elementary analysis only. Moreover, all the proofs are carried out in detail. These features make the book easily accessible to readers with only the mathematical training offered by undergraduate education in mathematics or in physics, and also ideal for individual study. The principles of quantum mechanics are discussed with complete mathematical accuracy and an effort is made to always trace them back to the experimental reality that lies at their root. The treatment of quantum mechanics is axiomatic, with definitions followed by propositions proved in a mathematical fashion. No previous knowledge of quantum mechanics is required. This book is designed so that parts of it can be easily used for various courses in mathematics and mathematical physics, as suggested in the Preface.The book is of interest to researchers and graduate students in functional analysis, who can see how closely an important part of their chosen field is linked with quantum mechanics, and also to physicists, who can see how the abstract language of functional analysis brings unity to the apparently distinct approaches employed in quantum theory.

An Introduction to Hilbert Space

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Publisher : Cambridge University Press
ISBN 13 : 9780521337175
Total Pages : 254 pages
Book Rating : 4.3/5 (371 download)

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Book Synopsis An Introduction to Hilbert Space by : N. Young

Download or read book An Introduction to Hilbert Space written by N. Young and published by Cambridge University Press. This book was released on 1988-07-21 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of a Hilbert space is a central idea in functional analysis and this text demonstrates its applications in numerous branches of pure and applied mathematics.

Introduction to Hilbert Space

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Publisher : American Mathematical Soc.
ISBN 13 : 0821819127
Total Pages : 226 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Introduction to Hilbert Space by : Sterling K. Berberian

Download or read book Introduction to Hilbert Space written by Sterling K. Berberian and published by American Mathematical Soc.. This book was released on 1999 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Preface: ``This textbook has evolved from a set of lecture notes ... In both the course and the book, I have in mind first- or second-year graduate students in Mathematics and related fields such as Physics ... It is necessary for the reader to have a foundation in advanced calculus which includes familiarity with: least upper bound (LUB) and greatest lower bound (GLB), the concept of function, $\epsilon$'s and their companion $\delta$'s, and basic properties of sequences of real and complex numbers (convergence, Cauchy's criterion, the Weierstrass-Bolzano theorem). It is not presupposed that the reader is acquainted with vector spaces ... , matrices ... , or determinants ... There are over four hundred exercises, most of them easy ... It is my hope that this book, aside from being an exposition of certain basic material on Hilbert space, may also serve as an introduction to other areas of functional analysis.''

Quantum Computation and Quantum Information

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Publisher : Cambridge University Press
ISBN 13 : 1139495488
Total Pages : 709 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Quantum Computation and Quantum Information by : Michael A. Nielsen

Download or read book Quantum Computation and Quantum Information written by Michael A. Nielsen and published by Cambridge University Press. This book was released on 2010-12-09 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most cited books in physics of all time, Quantum Computation and Quantum Information remains the best textbook in this exciting field of science. This 10th anniversary edition includes an introduction from the authors setting the work in context. This comprehensive textbook describes such remarkable effects as fast quantum algorithms, quantum teleportation, quantum cryptography and quantum error-correction. Quantum mechanics and computer science are introduced before moving on to describe what a quantum computer is, how it can be used to solve problems faster than 'classical' computers and its real-world implementation. It concludes with an in-depth treatment of quantum information. Containing a wealth of figures and exercises, this well-known textbook is ideal for courses on the subject, and will interest beginning graduate students and researchers in physics, computer science, mathematics, and electrical engineering.

Quantum Theory for Mathematicians

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Publisher : Springer Science & Business Media
ISBN 13 : 1461471168
Total Pages : 566 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Quantum Theory for Mathematicians by : Brian C. Hall

Download or read book Quantum Theory for Mathematicians written by Brian C. Hall and published by Springer Science & Business Media. This book was released on 2013-06-19 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.

Hilbert Space Operators in Quantum Physics

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Publisher : Springer Science & Business Media
ISBN 13 : 1402088701
Total Pages : 677 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Hilbert Space Operators in Quantum Physics by : Jirí Blank

Download or read book Hilbert Space Operators in Quantum Physics written by Jirí Blank and published by Springer Science & Business Media. This book was released on 2008-09-24 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new edition of this book detailing the theory of linear-Hilbert space operators and their use in quantum physics contains two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography contains 130 new items.

Quantum Logic in Algebraic Approach

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Publisher : Springer Science & Business Media
ISBN 13 : 9401590265
Total Pages : 244 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Quantum Logic in Algebraic Approach by : Miklós Rédei

Download or read book Quantum Logic in Algebraic Approach written by Miklós Rédei and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has grown out of the lecture notes that were prepared for a series of seminars on some selected topics in quantum logic. The seminars were delivered during the first semester of the 1993/1994 academic year in the Unit for Foundations of Science of the Department of History and Foundations of Mathematics and Science, Faculty of Physics, Utrecht University, The Netherlands, while I was staying in that Unit on a European Community Research Grant, and in the Center for Philosophy of Science, University of Pittsburgh, U. S. A. , where I was staying during the 1994/1995 academic year as a Visiting Fellow on a Fulbright Research Grant, and where I also was supported by the Istvan Szechenyi Scholarship Foundation. The financial support provided by these foundations, by the Center for Philosophy of Science and by the European Community is greatly acknowledged, and I wish to thank D. Dieks, the professor of the Foundations Group in Utrecht and G. Massey, the director of the Center for Philosophy of Science in Pittsburgh for making my stay at the respective institutions possible. I also wish to thank both the members of the Foundations Group in Utrecht, especially D. Dieks, C. Lutz, F. Muller, J. Uffink and P. Vermaas and the participants in the seminars at the Center for Philosophy of Science in Pittsburgh, especially N. Belnap, J. Earman, A. Janis, J. Norton, and J.

Introduction to Hilbert Space and the Theory of Spectral Multiplicity

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Publisher : Courier Dover Publications
ISBN 13 : 048682683X
Total Pages : 129 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Introduction to Hilbert Space and the Theory of Spectral Multiplicity by : Paul R. Halmos

Download or read book Introduction to Hilbert Space and the Theory of Spectral Multiplicity written by Paul R. Halmos and published by Courier Dover Publications. This book was released on 2017-11-15 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise introductory treatment consists of three chapters: The Geometry of Hilbert Space, The Algebra of Operators, and The Analysis of Spectral Measures. A background in measure theory is the sole prerequisite. 1957 edition.

An Introduction to Quantum Computing

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Publisher : Oxford University Press
ISBN 13 : 0198570007
Total Pages : 287 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis An Introduction to Quantum Computing by : Phillip Kaye

Download or read book An Introduction to Quantum Computing written by Phillip Kaye and published by Oxford University Press. This book was released on 2007 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors provide an introduction to quantum computing. Aimed at advanced undergraduate and beginning graduate students in these disciplines, this text is illustrated with diagrams and exercises.

Introduction to Hilbert Spaces with Applications

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Publisher : Elsevier
ISBN 13 : 0080455921
Total Pages : 599 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Introduction to Hilbert Spaces with Applications by : Lokenath Debnath

Download or read book Introduction to Hilbert Spaces with Applications written by Lokenath Debnath and published by Elsevier. This book was released on 2005-09-29 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, Third Edition, offers an overview of the basic ideas and results of Hilbert space theory and functional analysis. It acquaints students with the Lebesgue integral, and includes an enhanced presentation of results and proofs. Students and researchers will benefit from the wealth of revised examples in new, diverse applications as they apply to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation. The text also includes a popular chapter on wavelets that has been completely updated. Students and researchers agree that this is the definitive text on Hilbert Space theory. Updated chapter on wavelets Improved presentation on results and proof Revised examples and updated applications Completely updated list of references

Handbook of Quantum Logic and Quantum Structures

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Publisher : Elsevier
ISBN 13 : 008055038X
Total Pages : 821 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Quantum Logic and Quantum Structures by : Kurt Engesser

Download or read book Handbook of Quantum Logic and Quantum Structures written by Kurt Engesser and published by Elsevier. This book was released on 2011-08-11 with total page 821 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled “The logic of quantum mechanics quantum logic, i.e. the logical investigation of quantum mechanics, has undergone an enormous development. Various schools of thought and approaches have emerged and there are a variety of technical results.Quantum logic is a heterogeneous field of research ranging from investigations which may be termed logical in the traditional sense to studies focusing on structures which are on the border between algebra and logic. For the latter structures the term quantum structures is appropriate. The chapters of this Handbook, which are authored by the most eminent scholars in the field, constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic and quantum structures. Much of the material presented is of recent origin representing the frontier of the subject. The present volume focuses on quantum structures. Among the structures studied extensively in this volume are, just to name a few, Hilbert lattices, D-posets, effect algebras MV algebras, partially ordered Abelian groups and those structures underlying quantum probability. - Written by eminent scholars in the field of logic- A comprehensive presentation of the theory, approaches and results in the field of quantum logic- Volume focuses on quantum structures

A Primer on Hilbert Space Theory

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Author :
Publisher : Springer Nature
ISBN 13 : 3030674177
Total Pages : 343 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis A Primer on Hilbert Space Theory by : Carlo Alabiso

Download or read book A Primer on Hilbert Space Theory written by Carlo Alabiso and published by Springer Nature. This book was released on 2021-03-03 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an essential introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for providing an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, lies in the strenuous mathematics demands that even the simplest physical cases entail. Graduate courses in physics rarely offer enough time to cover the theory of Hilbert space and operators, as well as distribution theory, with sufficient mathematical rigor. Accordingly, compromises must be found between full rigor and the practical use of the instruments. Based on one of the authors’s lectures on functional analysis for graduate students in physics, the book will equip readers to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. It also includes a brief introduction to topological groups, and to other mathematical structures akin to Hilbert space. Exercises and solved problems accompany the main text, offering readers opportunities to deepen their understanding. The topics and their presentation have been chosen with the goal of quickly, yet rigorously and effectively, preparing readers for the intricacies of Hilbert space. Consequently, some topics, e.g., the Lebesgue integral, are treated in a somewhat unorthodox manner. The book is ideally suited for use in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.

Mathematical Foundations of Quantum Mechanics

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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

Quantum Mechanics in Hilbert Space

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Publisher : Academic Press
ISBN 13 : 0080873545
Total Pages : 670 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Quantum Mechanics in Hilbert Space by :

Download or read book Quantum Mechanics in Hilbert Space written by and published by Academic Press. This book was released on 2003-02-13 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Mechanics in Hilbert Space