AA 2023-24, William Borrelli, Davide Fermi

The course consists of two parts. General results for self-adjoint operators will be presented, with particular emphasis on Schrödinger operators, corresponding to quantum Hamiltonians of physical interest. We will first describe various approaches to the description of self-adjoint extensions of symmetric operators. Then we shall deal with different classifications of the spectrum of self-adjoint operators, presenting some results about stability under perturbations. The relation with the associated quantum dynamics will be presented. This subject will be further explored in the second part of the course, dealing with quantum scattering problems. We will focus mainly on the one-particle case, presenting the basic aspects of the theory, in both the time-independent and time-dependent formulations.