Effective One-Particle Equations for Correlated Many-Particle-(Coulomb) Systems: Derivation and Properties

We propose to derive effective one-particle equations for (fermionic) many particle systems. The emphasis will be on electrons that interact via Coulomb forces among each other and the nucleus. Both, the stationary and the dynamic case will be treated. In the stationary case the emphasis will be on relativistic Coulomb systems. in the dynamical case where there are few results for Coulomb systems even in the non-relativistic setting, we propose to develop mathematical methods which allow the treatment of Coulomb singularites. Finally, the effective one-particle equations will be investigated for the Coulomb case.

DFG Programme Research Grants