Valter Moretti Libri

Scopo principale di questo libro è quello di esporre i fondamenti matematici della Meccanica Quantistica (non relativistica) in modo matematicamente rigoroso. Il libro può considerarsi un testo introduttivo all’analisi funzionale lineare sugli spazi di Hilbert, con particolare enfasi su alcuni risultati di teoria spettrale. Le idee matematiche vengono sviluppate in modo astratto e logicamente indipendente dalla trattazione fisica, che appare comunque nelle motivazioni e nelle applicazioni. Inoltre, il libro si prefigge di raccogliere in un unico testo diversi utili risultati rigorosi, ma più avanzati di quanto si trovi nei manuali di fisica quantistica, sulla struttura matematica della Meccanica Quantistica.

Focused on classical Mathematical Physics, this textbook introduces key concepts such as Classical Mechanics, Lagrangian and Hamiltonian formulations, and significant theorems like Lyapunov stability and Poincaré recurrence. It rigorously explores Special Relativity through an axiomatic approach, emphasizing the logical-mathematical structure of the theories. The text highlights critical themes like Galilean and Poincaré symmetries, the interplay between symmetries and constants of motion, and the global description of Dynamics. Designed for flexibility, it caters to diverse curricula and student needs.

Focusing on advanced mathematical structures in quantum theory, this textbook offers a thorough exploration of the connections between logic, lattice theory, and probability. Designed for MSc students, it covers essential topics such as von Neumann algebras and the algebraic formulation relevant to quantum mechanics. The text also delves into hidden-variable interpretations, discussing significant results like Gleason's and the Kochen-Specker theorems, and examines concepts of realism and non-contextuality in relation to the Bell inequality.

Focusing on the mathematical foundations of quantum theories, this book serves as an introductory text on linear functional analysis, particularly emphasizing Hilbert spaces. It delves into spectral theory elements crucial for physics, while also examining physical phenomenology. The latter sections shift towards the formal and logical aspects of the theory, providing a comprehensive understanding of how mathematical principles underpin quantum mechanics.