Central to relativistic quantum mechanics is the Dirac equation, a partial differential equation that describes the dynamics of a spin- particle. When one studies such dynamics in the electrostatic field generated by a nuclear point charge placed at the origin, one has to face the problem of qualifying the self-adjoint realisation(s) of thne minimal Dirac-Coulomb operator. In this talk I will introduce the basic elements of the theory of unbounded linear operators on Hilbert spaces and present some recent results obtained in a joint work with Alessandro Michelangeli.

You can find the complete list of the AJS-seminars here: https://www.math.sissa.it/content/ajs-analysis-junior-seminars-2017-2018 .

We recall that this series of weekly seminars is intended to be an informal presentation of each student of the Analysis group, where he/she gives a general overview of his/her research with the other members of the group. Everyone is welcome. The spirit is: "Ask anything to understand everything!".