Università Roma Tre

The main goal of the course is to provide an elemantary but self-contained presentation of the Hilbert space formulation of quantum mechanics. Some standard notions and results of operator theory will be applied to the analysis of the simplest quantum systems (free particle and harmonic oscillator) as well as the definition of atomic hamiltonians and their spectral properties. The existence and uniqueness of ground and bound states will be discussed in details. The last part of the course will be devoted to the study of many-body quantum systems (Thomas-Fermi theory and stability of matter, Bose-Einstein condensation etc.).