Electron Wavefunctions and Densities for Atoms

Abstract

With a special `Ansatz' we analyse the regularity properties of atomic electron wavefunctions and electron densities. In particular we prove an a priori estimate, ${\sup }_{y\in B(x,R)}|\nabla \psi (y)|\le C(R){\sup }_{y\in B(x,2R)}|\psi (y)|$ and obtain for the spherically averaged electron density, $\tilde{\rho }(r)$, that ${\tilde{\rho }}^{\prime \prime }(0)$ exists and is non-negative.