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Spectral Theory and Quantum Mechanics

2018-01-30 Mathematics
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Release : 2018-01-30
Genre : Mathematics
Kind : eBook
Book Rating : 06X/5 ( reviews)

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Book Synopsis Spectral Theory and Quantum Mechanics by : Valter Moretti

Download or read book Spectral Theory and Quantum Mechanics written by Valter Moretti. This book was released on 2018-01-30. Available in PDF, EPUB and Kindle. Book excerpt: 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."

Intermediate Spectral Theory and Quantum Dynamics

2008-12-30 Science
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Release : 2008-12-30
Genre : Science
Kind : eBook
Book Rating : 955/5 ( reviews)

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Book Synopsis Intermediate Spectral Theory and Quantum Dynamics by : César R. de Oliveira

Download or read book Intermediate Spectral Theory and Quantum Dynamics written by César R. de Oliveira. This book was released on 2008-12-30. Available in PDF, EPUB and Kindle. Book excerpt: The spectral theory of linear operators plays a key role in the mathematical formulation of quantum theory. This textbook provides a concise and comprehensible introduction to the spectral theory of (unbounded) self-adjoint operators and its application in quantum dynamics. Many examples and exercises are included that focus on quantum mechanics.

Spectral Theory and Quantum Mechanics

2013-04-02 Mathematics
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Release : 2013-04-02
Genre : Mathematics
Kind : eBook
Book Rating : 353/5 ( reviews)

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Book Synopsis Spectral Theory and Quantum Mechanics by : Valter Moretti

Download or read book Spectral Theory and Quantum Mechanics written by Valter Moretti. This book was released on 2013-04-02. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quantum Theory for Mathematicians

2013-06-19 Science
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Release : 2013-06-19
Genre : Science
Kind : eBook
Book Rating : 168/5 ( reviews)

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Book Synopsis Quantum Theory for Mathematicians by : Brian C. Hall

Download or read book Quantum Theory for Mathematicians written by Brian C. Hall. This book was released on 2013-06-19. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spectral Methods in Quantum Field Theory

2009-05-08 Science
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Release : 2009-05-08
Genre : Science
Kind : eBook
Book Rating : 386/5 ( reviews)

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Book Synopsis Spectral Methods in Quantum Field Theory by : Noah Graham

Download or read book Spectral Methods in Quantum Field Theory written by Noah Graham. This book was released on 2009-05-08. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph we apply scattering theory methods to calculations in quantum ?eld theory, with a particular focus on properties of the quantum vacuum. These methods will provide e?cient and reliable solutions to a - riety of problems in quantum ?eld theory. Our approach will also elucidate in a concrete context many of the subtleties of quantum ?eld theory, such as divergences, regularization, and renormalization, by connecting them to more familiar results in quantum mechanics. We will use tools of scattering theory to characterize the spectrum of energyeigenstatesinapotentialbackground,hencethetermspectralmethods. This mode spectrum comprises both discrete bound states and a continuum of scattering states. We develop a powerful formalism that parameterizes the e?ects of the continuum by the density of states, which we compute from scattering data. Summing the zero-point energies of these modes gives the energy of the quantum vacuum, which is one of the central quantities we study.Althoughthemostcommonlystudiedbackgroundpotentialsarisefrom static soliton solutions to the classical equations of motion, these methods are not limited to such cases.

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