Spectral Theory and Quantum Mechanics : With an Introduction to the Algebraic Formulation / / by Valter Moretti
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| Autore: |
Moretti Valter
|
| Titolo: |
Spectral Theory and Quantum Mechanics : With an Introduction to the Algebraic Formulation / / by Valter Moretti
|
| Pubblicazione: | Milano : , : Springer Milan : , : Imprint : Springer, , 2013 |
| Edizione: | 1st ed. 2013. |
| Descrizione fisica: | 1 online resource (742 p.) |
| Disciplina: | 515.7222 |
| Soggetto topico: | Applied mathematics |
| Engineering mathematics | |
| Mathematical physics | |
| Physics | |
| Mathematical analysis | |
| Analysis (Mathematics) | |
| Applications of Mathematics | |
| Theoretical, Mathematical and Computational Physics | |
| Mathematical Methods in Physics | |
| Analysis | |
| Persona (resp. second.): | ChiossiSimon G. |
| Note generali: | "Translated and extended version of the original Italian edition: V. Moretti, Teoria spettrale e meccanica quantistica, ©Springer-Verlag Italia 2010"--Title page verso. |
| Nota di bibliografia: | Includes bibliographical references and index. |
| Nota di contenuto: | Introduction and mathematical backgrounds -- Normed and Banach spaces, examples and applications -- Hilbert spaces and bounded operators -- Families of compact operators on Hilbert spaces and fundamental properties -- Densely-defined unbounded operators on Hilbert spaces -- Phenomenology of quantum systems and Wave Mechanics: an overview -- The first 4 axioms of QM: propositions, quantum states and observables -- Spectral Theory I: generalities, abstract C -algebras and operators in B(H) -- Spectral theory II: unbounded operators on Hilbert spaces -- Spectral Theory III: applications -- Mathematical formulation of non-relativistic Quantum Mechanics -- Introduction to Quantum Symmetries -- Selected advanced topics in Quantum Mechanics -- Introduction to the Algebraic Formulation of Quantum Theories -- Order relations and groups -- Elements of differential geometry. |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | Spectral Theory and Quantum Mechanics |
| ISBN: | 88-470-2835-3 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910437871703321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
La Matematica per il 3+2, . 2038-5722