The eigenvalues of one-particle Dirac operator with general charge distributions
Tuesday 16 June 2020
For heavy atoms and molecules, relativistic effects have to be taken into account. The most precise option is to use the Dirac operator, but it is then notoriously difficult to include Coulomb potentials, which scale the same as the kinetic energy. In this talk I will discuss one-particle Dirac operators with the potential induced by an arbitrary charge distribution. I will particularly focus on min-max formulas for the eigenvalues and on an important conjecture about the optimality of the first Dirac eigenvalue. If true, this conjecture would have an impact on the shape of the potential energy surface of molecules in Dirac theory.