Spectral Theory and Quantum Mechanics Mathematical Foundations of Quantum Theories, Symmetries and Introduction to the Algebraic Formulation
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...
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| Format: | eBook |
| Language: | English |
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Cham
Springer International Publishing
2017, 2017
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| Edition: | 2nd ed. 2017 |
| Series: | La Matematica per il 3+2
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 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