Spectral Theory and Quantum Mechanics With an Introduction to the Algebraic Formulation /

• Main Author: Moretti, Valter. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Milano : Springer Milan : Imprint: Springer, 2013.
• Series: UNITEXT,
• Subjects: Mathematics.; Global analysis (Mathematics).; Mathematical physics.; Applications of Mathematics.; Theoretical, Mathematical and Computational Physics.; Mathematical Methods in Physics.; Analysis.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-88-470-2835-7

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 phys...

Table of Contents:

• 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.