Spectral Theory and Quantum Mechanics Mathematical Foundations of Quantum Theories, Symmetries and 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: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Έκδοση: 2nd ed. 2017.
• Σειρά: UNITEXT, 110
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Applied mathematics.; Engineering mathematics.; Physics.; Applications of Mathematics.; Mathematical Methods in Physics.; Analysis.

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 attenti...

Πίνακας περιεχομένων:

• 1 Introduction and Mathematical Backgrounds
• 2 Normed and Banach Spaces, Examples and Applications
• 3 Hilbert Spaces and Bounded Operators
• 4 Families of Compact Operators on Hilbert Spaces and Fundamental Properties
• 5 Densely-Defined Unbounded Operators on Hilbert Spaces
• 6 Phenomenology of Quantum Systems and Wave Mechanics: an Overview
• 7 The First 4 Axioms of QM: Propositions, Quantum States and Observables
• 8 Spectral Theory I: Generalities, Abstract C -algebras and Operators in B(H)
• 9 Spectral theory II: Unbounded Operators on Hilbert Spaces
• 10 Spectral Theory III: Applications
• 11 Mathematical Formulation of Non-Relativistic Quantum Mechanics
• 12 Introduction to Quantum Symmetries
• 13 Selected Advanced Topics in Quantum Mechanics
• 14 Introduction to the Algebraic Formulation of Quantum Theories
• 15 Appendix A: Order Relations and Groups
• 16 Appendix B: Elements of Differential Geometry.