About Schrödinger and Dirac operators with scaling critical potentials

par Luca Fanelli (Ikerbasque & Universidad del País Vasco)

mardi 11 mai 2021, 14:00 → 15:00 Europe/Paris

Fokko (ICJ)

Lower-order perturbations of the free Hamiltonians usually appear in Quantum Mechanics, as models describing the interaction of a free particle with an external field. In some cases, the perturbation lies at the same level as the free Hamiltonian, and the resulting conflict can generate interesting phenomena. We will introduce the Inverse Square and Coulomb potentials as toy models, and describe the main features of the complete Hamiltonians from the point of view of Fourier Analysis, Spectral Theory, and dispersive evolutions.