Diagonal Behaviour of the Density Matrix for Coulombic Wavefunctions

We consider the quantum system of N electrons in a field of nuclei. The eigenstates of the corresponding Hamiltonian represent the electronic states of an atom or molecule. Obtaining approximations to these eigenstates is an important goal in the field of quantum chemistry, and a key role in these approximation schemes is played by the one-particle reduced density matrix. In this talk I will present new analytic results concerning the differentiability properties of this density matrix for eigenstates. It is known that the density matrix is real analytic away from the nuclei and the diagonal. We study the non-smoothness at the diagonal using derivative bounds and find that up to five bounded derivatives exist at the diagonal.