Mathematical Structures Of Quantum Mechanics PDF Download
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| Author | : Chang Kow Lung |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 208 |
| Release | : 2011-10-31 |
| Genre | : Science |
| ISBN | : 9813108231 |
Download Mathematical Structures Of Quantum Mechanics Book in PDF, ePub and Kindle
This marvelous book is aimed at strengthening the mathematical background and sharpening the mathematical tools of students without rigorous training before taking the quantum mechanics course. The abstract construction of quantum postulates in the framework of Hilbert space and Hermitian operators are realized by q-representation in the formulation to demonstrate the conventional approach to quantum theory.Symmetry property is emphasized and extensively explored in this book both in continuous transformations as well as in the discrete ones. The space-time structure is discussed in depth and Dirac equation is formulated by symmetry consideration of Lorentz group.
| Author | : Valter Moretti |
| Publisher | : Springer |
| Total Pages | : 345 |
| Release | : 2019-06-20 |
| Genre | : Science |
| ISBN | : 3030183467 |
Download Fundamental Mathematical Structures of Quantum Theory Book in PDF, ePub and Kindle
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.
| Author | : F Strocchi |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 200 |
| Release | : 2008-10-30 |
| Genre | : Science |
| ISBN | : 9813107367 |
Download An Introduction to the Mathematical Structure of Quantum Mechanics Book in PDF, ePub and Kindle
The second printing contains a critical discussion of Dirac derivation of canonical quantization, which is instead deduced from general geometric structures. This book arises out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students. The mathematical structure of QM is formulated 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, for a general physical system. The Dirac–von Neumann axioms are then derived. The description of states and observables as Hilbert space vectors and operators follows from the GNS and Gelfand–Naimark Theorems. The experimental existence of complementary observables for atomic systems is shown to imply the noncommutativity of the observable algebra, the distinctive feature of QM; for finite degrees of freedom, the Weyl algebra codifies the experimental complementarity of position and momentum (Heisenberg commutation relations) and Schrödinger QM follows from the von Neumann uniqueness theorem. The existence problem of the dynamics is related to the self-adjointness of the Hamiltonian and solved by the Kato–Rellich conditions on the potential, which also guarantee quantum stability for classically unbounded-below Hamiltonians. 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), to the formulation in terms of ground state correlations (the quantum mechanical analog of the Wightman functions) and their analytic continuation to imaginary time (Euclidean QM). The quantum particle on a circle is discussed in detail, as an example of the interplay between topology and functional integral, leading to the emergence of superselection rules and θ sectors. Errata(s) Errata
| 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 | : 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 | : F. Strocchi |
| Publisher | : World Scientific |
| Total Pages | : 193 |
| Release | : 2008 |
| Genre | : Science |
| ISBN | : 9812835229 |
Download An Introduction to the Mathematical Structure of Quantum Mechanics Book in PDF, ePub and Kindle
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.
| Author | : Gregory L. Naber |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 507 |
| Release | : 2021-09-20 |
| Genre | : Science |
| ISBN | : 3110752042 |
Download Quantum Mechanics Book in PDF, ePub and Kindle
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.
| 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 | : 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 | : F Strocchi |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 160 |
| Release | : 2005-11-17 |
| Genre | : Science |
| ISBN | : 981310659X |
Download An Introduction to the Mathematical Structure of Quantum Mechanics Book in PDF, ePub and Kindle
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.
