Asymptotics for the Approximation of Wave Functions by Exponential-Sums Original Research Article

When studying the approximation of the wave functions of the H-atom by sums of Gaussians, Klopper and Kutzelnigg [KK] and Kutzelnigg [Ku] found an asymptotic of exp[−γ √n]. The results were obtained from numerical results and justified by some asymptotic expansions in quadrature formulas, We will verify the asymptotic behaviour by a very different method. We transform the given problem into an approximation problem of completely monotone functions by exponential sums. The approximation problem on an infinite interval is treated by using results from rational approximation.