Spectral Theory and Quantum Mechanics
With an Introduction to the Algebraic Formulation
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Beschreibung
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.
This mathematically rigorousm self-contained book explains the foundations of Quantum Mechanics and Quantum Theories in general. Includes a primer on general topology and abstract measure theory, along with material in the appendices on differential geometry.
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.
Most chapters are accompanied by exercises, many of which solved explicitly
At any rate several examples of the physical formalism are presented
Many of these aspects have been known for a long time but are scattered in the specialistic literature
Autor*in
Valter Moretti
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Functional Analysis on Hilbert Spaces Mathematical Physics Quantum Mechanics Spectral Theory
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From the reviews:
“The present text is an extended translation of its original Italian version published 2010 and gives a comprehensive introduction to the mathematical tools used in quantum mechanics. … The text is well-written and gives a self-contained and concise introduction to these topics. Many exercises make it suitable as a basis for various courses in this area.” (G. Teschl, Monatshefte für Mathematik, 2013)()