Abstract (EN)

This article is devoted to a two-spinor characterization of energy levels of Dirac operators based at a theoretical level on a rigorous variational method, with applications in atomic and molecular physics. This provides a numerical method that is free of the numerical drawbacks often present in discretized relativistic approaches. It is moreover independent of the geometry and monotone: Eigenvalues are approximated from above. We illustrate our numerical approach by the computation of the ground state in atomic and diatomic configurations using B-splines.