Abstract:

Numerical calculations of energy levels for large atoms or molecules is hindered by the large number of parameters. For instance, the eigenfunction associated with a bound state of an atom with $N$ electrons depends on $N$ three-dimensional variables. To simplify the calculations one introduces the one-particle density matrix which is built from the eigenfunction, but depends only on two three-dimensional variables. The aim of the talk is to present some analytic properties of the density matrix and to discuss the discrete spectrum of the operator whose kernel is given by the density matrix. A part of this work is joint with Peter Hearnshaw.