The Mathematical Language Of Quantum Theory

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The Mathematical Language of Quantum Theory

Teiko Heinosaari,Mário Ziman
The Mathematical Language of Quantum Theory Book PDF

Author : Teiko Heinosaari,Mário Ziman
Publisher : Cambridge University Press
Page : 340 pages
File Size : 50,7 Mb
Release : 2011-12-15
Category : Science
ISBN : 9781139503990

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The Mathematical Language of Quantum Theory by Teiko Heinosaari,Mário Ziman Pdf

For almost every student of physics, the first course on quantum theory raises a lot of puzzling questions and creates a very uncertain picture of the quantum world. This book presents a clear and detailed exposition of the fundamental concepts of quantum theory: states, effects, observables, channels and instruments. It introduces several up-to-date topics, such as state discrimination, quantum tomography, measurement disturbance and entanglement distillation. A separate chapter is devoted to quantum entanglement. The theory is illustrated with numerous examples, reflecting recent developments in the field. The treatment emphasises quantum information, though its general approach makes it a useful resource for graduate students and researchers in all subfields of quantum theory. Focusing on mathematically precise formulations, the book summarises the relevant mathematics.

Quantum Theory for Mathematicians

Brian C. Hall
Quantum Theory for Mathematicians Book PDF

Author : Brian C. Hall
Publisher : Springer Science & Business Media
Page : 554 pages
File Size : 52,6 Mb
Release : 2013-06-19
Category : Science
ISBN : 9781461471165

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Quantum Theory for Mathematicians by Brian C. Hall Pdf

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.

Mathematics of Classical and Quantum Physics

Frederick W. Byron,Robert W. Fuller
Mathematics of Classical and Quantum Physics Book PDF

Author : Frederick W. Byron,Robert W. Fuller
Publisher : Courier Corporation
Page : 674 pages
File Size : 55,7 Mb
Release : 2012-04-26
Category : Science
ISBN : 9780486135069

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Mathematics of Classical and Quantum Physics by Frederick W. Byron,Robert W. Fuller Pdf

Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.

Language, Quantum, Music

Maria Luisa Dalla Chiara,Roberto Giuntini,Federico Laudisa
Language Quantum Music Book PDF

Author : Maria Luisa Dalla Chiara,Roberto Giuntini,Federico Laudisa
Publisher : Springer Science & Business Media
Page : 339 pages
File Size : 48,7 Mb
Release : 2013-04-17
Category : Science
ISBN : 9789401720434

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Language, Quantum, Music by Maria Luisa Dalla Chiara,Roberto Giuntini,Federico Laudisa Pdf

A vivid and comprehensive picture of the current state of research in all directions of logic and philosophy of science. The book presents a wide combination of papers containing relevant technical results in the foundations of science and papers devoted to conceptual analyses, deeply rooted in advanced present-day research. Audience: The volume is attractive both for specialists in foundational questions and scholars interested in general epistemology.

The Mathematical Principles of Quantum Mechanics

Derek F. Lawden
The Mathematical Principles of Quantum Mechanics Book PDF

Author : Derek F. Lawden
Publisher : Courier Corporation
Page : 306 pages
File Size : 51,8 Mb
Release : 2005-01-01
Category : Science
ISBN : 9780486442235

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The Mathematical Principles of Quantum Mechanics by Derek F. Lawden Pdf

Focusing on the principles of quantum mechanics, this text for upper-level undergraduates and graduate students introduces and resolves special physical problems with more than 100 exercises. 1967 edition.

An Introductory Path to Quantum Theory

Stephen Bruce Sontz
An Introductory Path to Quantum Theory Book PDF

Author : Stephen Bruce Sontz
Publisher : Springer Nature
Page : 299 pages
File Size : 52,8 Mb
Release : 2020-03-16
Category : Science
ISBN : 9783030407674

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An Introductory Path to Quantum Theory by Stephen Bruce Sontz Pdf

Since the 17th century, physical theories have been expressed in the language of mathematical equations. This introduction to quantum theory uses that language to enable the reader to comprehend the notoriously non-intuitive ideas of quantum physics. The mathematical knowledge needed for using this book comes from standard undergraduate mathematics courses and is described in detail in the section Prerequisites. This text is especially aimed at advanced undergraduate and graduate students of mathematics, computer science, engineering and chemistry among other disciplines, provided they have the math background even though lacking preparation in physics. In fact, no previous formal study of physics is assumed.

Mathematical Methods in Quantum Mechanics

Gerald Teschl
Mathematical Methods in Quantum Mechanics Book PDF

Author : Gerald Teschl
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 55,9 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821846605

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Mathematical Methods in Quantum Mechanics by Gerald Teschl Pdf

Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem is a central topic in this approach and is introduced at an early stage. Part 2 starts with the free Schrodinger equation and computes the free resolvent and time evolution. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory. This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional analysis and no Lebesgue integration theory are assumed. It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature. It is well suited for self-study and includes numerous exercises (many with hints).

Mathematical Foundations of Quantum Mechanics

John von Neumann
Mathematical Foundations of Quantum Mechanics Book PDF

Author : John von Neumann
Publisher : Princeton University Press
Page : 462 pages
File Size : 55,8 Mb
Release : 1955
Category : Mathematics
ISBN : 0691028931

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Mathematical Foundations of Quantum Mechanics by John von Neumann Pdf

A revolutionary book that for the first time provided a rigorous mathematical framework for quantum mechanics. -- Google books

Quantum Mechanics and Quantum Field Theory

Jonathan Dimock
Quantum Mechanics and Quantum Field Theory Book PDF

Author : Jonathan Dimock
Publisher : Cambridge University Press
Page : 239 pages
File Size : 54,6 Mb
Release : 2011-02-03
Category : Science
ISBN : 9781139497480

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Quantum Mechanics and Quantum Field Theory by Jonathan Dimock Pdf

Explaining the concepts of quantum mechanics and quantum field theory in a precise mathematical language, this textbook is an ideal introduction for graduate students in mathematics, helping to prepare them for further studies in quantum physics. The textbook covers topics that are central to quantum physics: non-relativistic quantum mechanics, quantum statistical mechanics, relativistic quantum mechanics and quantum field theory. There is also background material on analysis, classical mechanics, relativity and probability. Each topic is explored through a statement of basic principles followed by simple examples. Around 100 problems throughout the textbook help readers develop their understanding.

Quantum Mechanics and Quantum Field Theory

Jonathan Dimock
Quantum Mechanics and Quantum Field Theory Book PDF

Author : Jonathan Dimock
Publisher : Unknown
Page : 240 pages
File Size : 42,8 Mb
Release : 2014-05-14
Category : Quantum theory
ISBN : 1139010336

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Quantum Mechanics and Quantum Field Theory by Jonathan Dimock Pdf

Explaining the concepts of quantum mechanics and quantum field theory in a precise mathematical language, this textbook is an ideal introduction for graduate students in mathematics, helping to prepare them for further studies in quantum physics. The textbook covers topics that are central to quantum physics: non-relativistic quantum mechanics, quantum statistical mechanics, relativistic quantum mechanics and quantum field theory. There is also background material on analysis, classical mechanics, relativity and probability. Each topic is explored through a statement of basic principles followed by simple examples. Around 100 problems throughout the textbook help readers develop their understanding.

Hilbert Space and Quantum Mechanics

Franco Gallone
Hilbert Space and Quantum Mechanics Book PDF

Author : Franco Gallone
Publisher : World Scientific Publishing Company
Page : 760 pages
File Size : 47,7 Mb
Release : 2014-12-23
Category : Science
ISBN : 9789814635851

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Hilbert Space and Quantum Mechanics by Franco Gallone Pdf

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.

Mathematical Foundations of Quantum Theory

A.R. Marlow
Mathematical Foundations of Quantum Theory Book PDF

Author : A.R. Marlow
Publisher : Elsevier
Page : 382 pages
File Size : 42,7 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780323141185

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Mathematical Foundations of Quantum Theory by A.R. Marlow Pdf

Mathematical Foundations of Quantum Theory is a collection of papers presented at the 1977 conference on the Mathematical Foundations of Quantum Theory, held in New Orleans. The contributors present their topics from a wide variety of backgrounds and specialization, but all shared a common interest in answering quantum issues. Organized into 20 chapters, this book's opening chapters establish a sound mathematical basis for quantum theory and a mode of observation in the double slit experiment. This book then describes the Lorentz particle system and other mathematical structures with which fundamental quantum theory must deal, and then some unsolved problems in the quantum logic approach to the foundations of quantum mechanics are considered. Considerable chapters cover topics on manuals and logics for quantum mechanics. This book also examines the problems in quantum logic, and then presents examples of their interpretation and relevance to nonclassical logic and statistics. The accommodation of conventional Fermi-Dirac and Bose-Einstein statistics in quantum mechanics or quantum field theory is illustrated. The final chapters of the book present a system of axioms for nonrelativistic quantum mechanics, with particular emphasis on the role of density operators as states. Specific connections of this theory with other formulations of quantum theory are also considered. These chapters also deal with the determination of the state of an elementary quantum mechanical system by the associated position and momentum distribution. This book is of value to physicists, mathematicians, and researchers who are interested in quantum theory.

MATHEMATICAL CONCEPTS OF QUANTUM MECHANICS

STEPHEN J. GUSTAFSON
MATHEMATICAL CONCEPTS OF QUANTUM MECHANICS Book PDF

Author : STEPHEN J. GUSTAFSON
Publisher : Unknown
Page : 128 pages
File Size : 45,5 Mb
Release : 2020
Category : Mathematics
ISBN : 9783030595623

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MATHEMATICAL CONCEPTS OF QUANTUM MECHANICS by STEPHEN J. GUSTAFSON Pdf

The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include: many-body systems, modern perturbation theory, path integrals, the theory of resonances, adiabatic theory, geometrical phases, Aharonov-Bohm effect, density functional theory, open systems, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. Some of the sections could be used for introductions to geometrical methods in Quantum Mechanics, to quantum information theory and to quantum electrodynamics and quantum field theory.

Lectures on Quantum Theory

C. J. Isham
Lectures on Quantum Theory Book PDF

Author : C. J. Isham
Publisher : Imperial College Press
Page : 220 pages
File Size : 52,6 Mb
Release : 1995-01-01
Category : Mathematics
ISBN : 1860940013

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Lectures on Quantum Theory by C. J. Isham Pdf

This book is based on material taught to final-year physics undergraduates as part of the theoretical physics option at Imperial College. After a self-contained introduction to the essential ideas of vector spaces and linear operators, a bridge is built between the concepts and mathematics of classical physics, and the new mathematical framework employed in quantum mechanics. The axioms of nonrelativistic quantum theory are introduced, and shown to lead to a variety of new conceptual problems. Subjects discussed include state-vector reduction, the problem of measurement, quantum entanglement, the Kochen-Specker theorem, and the Bell inequalities. The book includes twenty-five problems with worked solutions. In the US it could serve as an excellent supplement for an introductory graduate course on quantum mechanics ... The discursive style and clear exposition make for equally attractive reading by someone familiar with the subject or by a student with only rudimentary knowledge .... The main text is supplemented by a substantial number of problems with solutions, which should help the beginner master the mathematics .. I would strongly recommend that anyone teaching the subject use this little book as supplementary reading". Physics Today (USA), Aug 1996 "The proper role of mathematics is to make things easy. When something can be expressed in the precise language of mathematics, results can be obtained by the application of given rules. Calculations are so simple that even computers can do them. Chris Isham's lectures on the mathematical and structural foundations of quantum theory, reproduced in this book, provide an excellent illustration of this truth ... a welcome addition tothe modern literature on quantum theory ... It is good to have a book that gives such an excellent description of the mathematical structure of quantum theory ..". Times Higher Educational Supp. (UK), 1996

Categories for Quantum Theory

Chris Heunen,Jamie Vicary
Categories for Quantum Theory Book PDF

Author : Chris Heunen,Jamie Vicary
Publisher : Oxford University Press
Page : 320 pages
File Size : 41,8 Mb
Release : 2019-11-14
Category : Mathematics
ISBN : 9780191060069

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Categories for Quantum Theory by Chris Heunen,Jamie Vicary Pdf

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.