Explore spectral results and open problems for Dirac-Coulomb operators with general charge distributions in this 49-minute lecture by Maria J. Esteban from CNRS and Université Paris-Dauphine. Delve into recent findings on Dirac-Coulomb operators with Coulomb-like potentials, examining distinguished self-adjoint extensions and min-max characterizations of eigenvalues. Investigate the challenges in determining the location of the lowest eigenvalue within the spectral gap and the conditions necessary to prevent electron destabilization. Cover topics including the Dirac operator, theorems, quadratic forms, discretization algorithms, computational methods, operator domains, potentials, and molecule applications. Conclude with a discussion of open problems in the field of relativistic quantum mechanics.