Ebook: Spectral theory and quantum mechanics : with an introduction to the algebraic formulation

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