Seminar Analysis: Thomas Sørensen (Ludwig Maximilian University of Munich)

Properties of Coulombic eigenfunctions of atoms and molecules

The eigenfunctions of the Schrödinger operator for (non-relativistic) atoms and molecules (in the Born-Oppenheimer/clamped nuclei approximation) are solutions of an elliptic partial differential equation with singular (total) potential (i.e., zero-order term). In this talk we give an overview over our results about the structure/regularity of the eigenfunctions at the singularities of the potential. These, in particular, improve on the well-known ’Kato Cusp Condition’. If time permits, we also discuss the implications for the electron density.

This is joint work with S. Fournais (Aarhus, Denmark), and M. and T. Hoffmann-Ostenhof (Vienna, Austria).

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