An Introduction To The Mathematical Structure Of Quantum Mechanics
DOWNLOAD eBooks
Download An Introduction To The Mathematical Structure Of Quantum Mechanics PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get An Introduction To The Mathematical Structure Of Quantum Mechanics book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
An Introduction To The Mathematical Structure Of Quantum Mechanics
DOWNLOAD eBooks
Author : F. Strocchi
language : en
Publisher: World Scientific
Release Date : 2008
An Introduction To The Mathematical Structure Of Quantum Mechanics written by F. Strocchi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
Arising out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students, this book formulates the mathematical structure of QM in terms of the C*-algebra of observables, which is argued on the basis of the operational definition of measurements and the duality between states and observables.
An Introduction To The Mathematical Structure Of Quantum Mechanics
DOWNLOAD eBooks
Author : F Strocchi
language : en
Publisher: World Scientific Publishing Company
Release Date : 2005-11-17
An Introduction To The Mathematical Structure Of Quantum Mechanics written by F Strocchi and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-17 with Science categories.
This book arises out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students. Rather than starting from the Dirac–Von Neumann axioms, the book offers a short presentation of the mathematical structure of QM using the C–-algebraic structure of the observable based on the operational definition of measurements and the duality between states and observables. The description of states and observables as Hilbert space vectors and operators is then derived from the GNS and Gelfand-Naimark Theorems. For finite degrees of freedom, the Weyl algebra codifies the experimental limitations on the measurements of position and momentum (Heisenberg uncertainty relations) and Schroedinger QM follows from the von Neumann uniqueness theorem. The existence problem of the dynamics is related to the self-adjointness of the differential operator describing the Hamiltonian and solved by the Rellich–Kato theorems. Examples are discussed which include the explanation of the discreteness of the atomic spectra. Because of the increasing interest in the relation between QM and stochastic processes, a final chapter is devoted to the functional integral approach (Feynman–Kac formula), the formulation in terms of ground state correlations (Wightman functions) and their analytic continuation to imaginary time (Euclidean QM). The quantum particle on a circle as an example of the interplay between topology and functional integral is also discussed in detail.
An Introduction To The Mathematical Structure Of Quantum Mechanics
DOWNLOAD eBooks
Author : Franco Strocchi
language : en
Publisher:
Release Date : 2008
An Introduction To The Mathematical Structure Of Quantum Mechanics written by Franco Strocchi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Electronic books categories.
Quantum Mechanics
DOWNLOAD eBooks
Author : Gregory L. Naber
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-09-20
Quantum Mechanics written by Gregory L. Naber and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-20 with Science categories.
This work covers quantum mechanics by answering questions such as where did the Planck constant and Heisenberg algebra come from, what motivated Feynman to introduce his path integral and why does one distinguish two types of particles, the bosons and fermions. The author addresses all these topics with utter mathematical rigor. The high number of instructive Appendices and numerous Remark sections supply the necessary background knowledge.
Lectures On The Mathematics Of Quantum Mechanics I
DOWNLOAD eBooks
Author : Gianfausto Dell'Antonio
language : en
Publisher: Springer
Release Date : 2015-05-25
Lectures On The Mathematics Of Quantum Mechanics I written by Gianfausto Dell'Antonio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-25 with Science categories.
The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics.
Mathematical Foundations Of Quantum Mechanics
DOWNLOAD eBooks
Author : John von Neumann
language : en
Publisher: Princeton University Press
Release Date : 1955
Mathematical Foundations Of Quantum Mechanics written by John von Neumann and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1955 with Mathematics categories.
A revolutionary book that for the first time provided a rigorous mathematical framework for quantum mechanics. -- Google books
Fundamental Mathematical Structures Of Quantum Theory
DOWNLOAD eBooks
Author : Valter Moretti
language : en
Publisher: Springer
Release Date : 2019-06-20
Fundamental Mathematical Structures Of Quantum Theory written by Valter Moretti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-20 with Science categories.
This textbook presents in a concise and self-contained way the advanced fundamental mathematical structures in quantum theory. It is based on lectures prepared for a 6 months course for MSc students. The reader is introduced to the beautiful interconnection between logic, lattice theory, general probability theory, and general spectral theory including the basic theory of von Neumann algebras and of the algebraic formulation, naturally arising in the study of the mathematical machinery of quantum theories. Some general results concerning hidden-variable interpretations of QM such as Gleason's and the Kochen-Specker theorems and the related notions of realism and non-contextuality are carefully discussed. This is done also in relation with the famous Bell (BCHSH) inequality concerning local causality. Written in a didactic style, this book includes many examples and solved exercises. The work is organized as follows. Chapter 1 reviews some elementary facts and properties of quantum systems. Chapter 2 and 3 present the main results of spectral analysis in complex Hilbert spaces. Chapter 4 introduces the point of view of the orthomodular lattices' theory. Quantum theory form this perspective turns out to the probability measure theory on the non-Boolean lattice of elementary observables and Gleason's theorem characterizes all these measures. Chapter 5 deals with some philosophical and interpretative aspects of quantum theory like hidden-variable formulations of QM. The Kochen-Specker theorem and its implications are analyzed also in relation BCHSH inequality, entanglement, realism, locality, and non-contextuality. Chapter 6 focuses on the algebra of observables also in the presence of superselection rules introducing the notion of von Neumann algebra. Chapter 7 offers the idea of (groups of) quantum symmetry, in particular, illustrated in terms of Wigner and Kadison theorems. Chapter 8 deals with the elementary ideas and results of the so called algebraic formulation of quantum theories in terms of both *-algebras and C*-algebras. This book should appeal to a dual readership: on one hand mathematicians that wish to acquire the tools that unlock the physical aspects of quantum theories; on the other physicists eager to solidify their understanding of the mathematical scaffolding of quantum theories.
Mathematical Concepts Of Quantum Mechanics
DOWNLOAD eBooks
Author : STEPHEN J. GUSTAFSON
language : en
Publisher:
Release Date : 2020
Mathematical Concepts Of Quantum Mechanics written by STEPHEN J. GUSTAFSON and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Mathematics categories.
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.
Spectral Theory And Quantum Mechanics
DOWNLOAD eBooks
Author : Valter Moretti
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-02
Spectral Theory And Quantum Mechanics written by Valter Moretti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-02 with Mathematics categories.
This book pursues the accurate study of the mathematical foundations of Quantum Theories. It may be considered an introductory text on linear functional analysis with a focus on Hilbert spaces. Specific attention is given to spectral theory features that are relevant in physics. Having left the physical phenomenology in the background, it is the formal and logical aspects of the theory that are privileged. Another not lesser purpose is to collect in one place a number of useful rigorous statements on the mathematical structure of Quantum Mechanics, including some elementary, yet fundamental, results on the Algebraic Formulation of Quantum Theories. In the attempt to reach out to Master's or 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 should benefit established researchers to organise and present the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly.
Lectures On Quantum Theory Mathematical And Structural Foundations
DOWNLOAD eBooks
Author : Isham Chris J
language : en
Publisher: World Scientific
Release Date : 1995-09-01
Lectures On Quantum Theory Mathematical And Structural Foundations written by Isham Chris J and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-01 with Science categories.
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.