Emergence Of The Quantum From The Classical: Mathematical Aspects Of Quantum Processes PDF Download
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Author: Maurice A De Gosson
Publisher: World Scientific
ISBN: 1786344165
Category : Science
Languages : en
Pages : 306
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Book Description
The emergence of quantum mechanics from classical world mechanics is now a well-established theme in mathematical physics. This book demonstrates that quantum mechanics can indeed be viewed as a refinement of Hamiltonian mechanics, and builds on the work of George Mackey in relation to their mathematical foundations. Additionally when looking at the differences with classical mechanics, quantum mechanics crucially depends on the value of Planck's constant h. Recent cosmological observations tend to indicate that not only the fine structure constant α but also h might have varied in both time and space since the Big Bang. We explore the mathematical and physical consequences of a variation of h; surprisingly we see that a decrease of h leads to transitions from the quantum to the classical.Emergence of the Quantum from the Classical provides help to undergraduate and graduate students of mathematics, physics and quantum theory looking to advance into research in the field.
Author: Maurice A De Gosson
Publisher: World Scientific
ISBN: 1786344165
Category : Science
Languages : en
Pages : 306
Get Book Here
Book Description
The emergence of quantum mechanics from classical world mechanics is now a well-established theme in mathematical physics. This book demonstrates that quantum mechanics can indeed be viewed as a refinement of Hamiltonian mechanics, and builds on the work of George Mackey in relation to their mathematical foundations. Additionally when looking at the differences with classical mechanics, quantum mechanics crucially depends on the value of Planck's constant h. Recent cosmological observations tend to indicate that not only the fine structure constant α but also h might have varied in both time and space since the Big Bang. We explore the mathematical and physical consequences of a variation of h; surprisingly we see that a decrease of h leads to transitions from the quantum to the classical.Emergence of the Quantum from the Classical provides help to undergraduate and graduate students of mathematics, physics and quantum theory looking to advance into research in the field.
Author: Daniel F. Styer
Publisher: Cambridge University Press
ISBN: 1316101878
Category : Science
Languages : en
Pages : 248
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Book Description
This is an exceptionally accessible, accurate, and non-technical introduction to quantum mechanics. After briefly summarizing the differences between classical and quantum behaviour, this engaging account considers the Stern-Gerlach experiment and its implications, treats the concepts of probability, and then discusses the Einstein-Podolsky-Rosen paradox and Bell's theorem. Quantal interference and the concept of amplitudes are introduced and the link revealed between probabilities and the interference of amplitudes. Quantal amplitude is employed to describe interference effects. Final chapters explore exciting new developments in quantum computation and cryptography, discover the unexpected behaviour of a quantal bouncing-ball, and tackle the challenge of describing a particle with no position. Thought-provoking problems and suggestions for further reading are included. Suitable for use as a course text, The Strange World of Quantum Mechanics enables students to develop a genuine understanding of the domain of the very small. It will also appeal to general readers seeking intellectual adventure.
Author: Bob Coecke
Publisher: Cambridge University Press
ISBN: 1108107710
Category : Science
Languages : en
Pages : 847
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Book Description
The unique features of the quantum world are explained in this book through the language of diagrams, setting out an innovative visual method for presenting complex theories. Requiring only basic mathematical literacy, this book employs a unique formalism that builds an intuitive understanding of quantum features while eliminating the need for complex calculations. This entirely diagrammatic presentation of quantum theory represents the culmination of ten years of research, uniting classical techniques in linear algebra and Hilbert spaces with cutting-edge developments in quantum computation and foundations. Written in an entertaining and user-friendly style and including more than one hundred exercises, this book is an ideal first course in quantum theory, foundations, and computation for students from undergraduate to PhD level, as well as an opportunity for researchers from a broad range of fields, from physics to biology, linguistics, and cognitive science, to discover a new set of tools for studying processes and interaction.
Author: Frederick W. Byron
Publisher: Courier Corporation
ISBN: 0486135063
Category : Science
Languages : en
Pages : 674
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Book Description
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.
Author: Maurice A. de Gosson
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110722771
Category : Mathematics
Languages : en
Pages : 240
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Book Description
Quantum mechanics is arguably one of the most successful scientific theories ever and its applications to chemistry, optics, and information theory are innumerable. This book provides the reader with a rigorous treatment of the main mathematical tools from harmonic analysis which play an essential role in the modern formulation of quantum mechanics. This allows us at the same time to suggest some new ideas and methods, with a special focus on topics such as the Wigner phase space formalism and its applications to the theory of the density operator and its entanglement properties. This book can be used with profit by advanced undergraduate students in mathematics and physics, as well as by confirmed researchers.
Author: Michael Spivak
Publisher:
ISBN: 9780914098324
Category : Mechanics
Languages : en
Pages : 733
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Book Description
Author: Mark S. Swanson
Publisher: Courier Corporation
ISBN: 0486493067
Category : Science
Languages : en
Pages : 463
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Book Description
Graduate-level, systematic presentation of path integral approach to calculating transition elements, partition functions, and source functionals. Covers Grassmann variables, field and gauge field theory, perturbation theory, and nonperturbative results. 1992 edition.
Author: Pavel Bóna
Publisher: Springer Nature
ISBN: 3030450708
Category : Science
Languages : en
Pages : 243
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Book Description
This book investigates two possibilities for describing classical-mechanical physical systems along with their Hamiltonian dynamics in the framework of quantum mechanics.The first possibility consists in exploiting the geometrical properties of the set of quantum pure states of "microsystems" and of the Lie groups characterizing the specific classical system. The second approach is to consider quantal systems of a large number of interacting subsystems – i.e. macrosystems, so as to study the quantum mechanics of an infinite number of degrees of freedom and to look for the behaviour of their collective variables. The final chapter contains some solvable models of “quantum measurement" describing dynamical transitions from "microsystems" to "macrosystems".
Author: Arkady Plotnitsky
Publisher: Springer
ISBN: 3319320688
Category : Science
Languages : en
Pages : 341
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Book Description
The book considers foundational thinking in quantum theory, focusing on the role the fundamental principles and principle thinking there, including thinking that leads to the invention of new principles, which is, the book contends, one of the ultimate achievements of theoretical thinking in physics and beyond. The focus on principles, prominent during the rise and in the immediate aftermath of quantum theory, has been uncommon in more recent discussions and debates concerning it. The book argues, however, that exploring the fundamental principles and principle thinking is exceptionally helpful in addressing the key issues at stake in quantum foundations and the seemingly interminable debates concerning them. Principle thinking led to major breakthroughs throughout the history of quantum theory, beginning with the old quantum theory and quantum mechanics, the first definitive quantum theory, which it remains within its proper (nonrelativistic) scope. It has, the book also argues, been equally important in quantum field theory, which has been the frontier of quantum theory for quite a while now, and more recently, in quantum information theory, where principle thinking was given new prominence. The approach allows the book to develop a new understanding of both the history and philosophy of quantum theory, from Planck’s quantum to the Higgs boson, and beyond, and of the thinking the key founding figures, such as Einstein, Bohr, Heisenberg, Schrödinger, and Dirac, as well as some among more recent theorists. The book also extensively considers the nature of quantum probability, and contains a new interpretation of quantum mechanics, “the statistical Copenhagen interpretation.” Overall, the book’s argument is guided by what Heisenberg called “the spirit of Copenhagen,” which is defined by three great divorces from the preceding foundational thinking in physics—reality from realism, probability from causality, and locality from relativity—and defined the fundamental principles of quantum theory accordingly.
Author: Leon Armenovich Takhtadzhi͡an
Publisher: American Mathematical Soc.
ISBN: 0821846302
Category : Mathematics
Languages : en
Pages : 410
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Book Description
Presents a comprehensive treatment of quantum mechanics from a mathematics perspective. Including traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin.
