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

• Κύριος συγγραφέας: Moretti, Valter (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Milano : Springer Milan : Imprint: Springer, 2013.
• Σειρά: UNITEXT,
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Applied mathematics.; Engineering mathematics.; Physics.; Applications of Mathematics.; Theoretical, Mathematical and Computational Physics.; Mathematical Methods in Physics.; Analysis.

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...

Πίνακας περιεχομένων:

• 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.