QLunch: Peter Hearnshaw

Speaker: Peter Hearnshaw, University College London

Title: Diagonal Behaviour of the Density Matrix for Coulombic Wavefunctions

Abstract: We consider the quantum system of N electrons in a fixed field of nuclei under a Coulombic interaction. A key role in approximation schemes for the energy eigenstates 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.