The Mathematical Language Of Quantum Theory PDF Download
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Author | : Teiko Heinosaari |
Publisher | : Cambridge University Press |
Total Pages | : 340 |
Release | : 2011-12-15 |
Genre | : Science |
ISBN | : 1139503995 |
Download The Mathematical Language of Quantum Theory Book in PDF, ePub and Kindle
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.
Author | : Brian C. Hall |
Publisher | : Springer Science & Business Media |
Total Pages | : 566 |
Release | : 2013-06-19 |
Genre | : Science |
ISBN | : 1461471168 |
Download Quantum Theory for Mathematicians Book in PDF, ePub and Kindle
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.
Author | : Frederick W. Byron |
Publisher | : Courier Corporation |
Total Pages | : 674 |
Release | : 2012-04-26 |
Genre | : Science |
ISBN | : 0486135063 |
Download Mathematics of Classical and Quantum Physics Book in PDF, ePub and Kindle
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 | : Derek F. Lawden |
Publisher | : Courier Corporation |
Total Pages | : 306 |
Release | : 2005-01-01 |
Genre | : Science |
ISBN | : 0486442233 |
Download The Mathematical Principles of Quantum Mechanics Book in PDF, ePub and Kindle
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.
Author | : Gerald Teschl |
Publisher | : American Mathematical Soc. |
Total Pages | : 322 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 0821846604 |
Download Mathematical Methods in Quantum Mechanics Book in PDF, ePub and Kindle
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).
Author | : John von Neumann |
Publisher | : Princeton University Press |
Total Pages | : 462 |
Release | : 1955 |
Genre | : Mathematics |
ISBN | : 9780691028934 |
Download Mathematical Foundations of Quantum Mechanics Book in PDF, ePub and Kindle
A revolutionary book that for the first time provided a rigorous mathematical framework for quantum mechanics. -- Google books
Author | : STEPHEN J. GUSTAFSON |
Publisher | : |
Total Pages | : |
Release | : 2020 |
Genre | : Mathematics |
ISBN | : 3030595625 |
Download MATHEMATICAL CONCEPTS OF QUANTUM MECHANICS Book in PDF, ePub and Kindle
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.
Author | : Valter Moretti |
Publisher | : Springer |
Total Pages | : 950 |
Release | : 2018-01-30 |
Genre | : Mathematics |
ISBN | : 331970706X |
Download Spectral Theory and Quantum Mechanics Book in PDF, ePub and Kindle
This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory. Further, this Second Edition collects in one volume a number of useful rigorous results on the mathematical structure of quantum mechanics focusing in particular on von Neumann algebras, Superselection rules, the various notions of Quantum Symmetry and Symmetry Groups, and including a number of fundamental results on the algebraic formulation of quantum theories. Intended for Master's and PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book also benefits established researchers by organizing and presenting the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly."
Author | : Jonathan Dimock |
Publisher | : Cambridge University Press |
Total Pages | : 239 |
Release | : 2011-02-03 |
Genre | : Science |
ISBN | : 1139497480 |
Download Quantum Mechanics and Quantum Field Theory Book in PDF, ePub and Kindle
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.
Author | : Enrico G. Beltrametti |
Publisher | : Cambridge University Press |
Total Pages | : 340 |
Release | : 2010-12-09 |
Genre | : Mathematics |
ISBN | : 9780521168496 |
Download The Logic of Quantum Mechanics: Volume 15 Book in PDF, ePub and Kindle
This volume examines the logic, theory and mathematics of quantum mechanics in a clear and thorough way.