MATHEMATICAL METHODS OF PHYSICS II
Learning outcomes of the course unit
Introduce the student to the basic concepts and to the methods of calculation of Quantum Mechanics
Course contents summary
Metric spaces, completeness, separability and completion. Vector, normed and Banach spaces, strong convergence. Unitary and Hilbert spaces, weak convergence, orthonormal systems and isomorphism with l_2 or C^n. Lebesgue integral, L_1 and L_2 spaces. Linear functionals, Riesz theorem, Dirac formalism. Limited linear operators, adjoint operator, isometric and unitary operators, projectors, invariant subspaces. Non-limited linear operators, operator graph,closed, symmetrical and self-adjoint operators. Spectral theory, resolving operator, operator spectrum. Decomposition and functions of operators, Stone theorem. Application to Quantum Mechanics, position and moment operators, creation and destruction operators.
Kolmogorov Fomin - Elementi di teoria delle funzioni e di analisi funzionale, Ed. Mir 1980
Bernardini Ragnisco Santini - Metodi matematici della fisica,
La Nuova Italia 1994
Abbati Cirelli - Metodi matematici per la fisica, Citta' Studi Ed. 1997
Onofri - Teoria degli o peratori lineari, Ed. Zara 1984
Fano - Metodi matematici della meccanica quantistica, Zanichelli 1967
Classroom lectures and exercices that are an integral part of them.
The examination includes a written test for admission to the subsequent oral test.