Discrete sets of many‐body Sturmians

In this work, we present a method to obtain two‐particle Coulomb Sturmians Functions (CSF) with an expansion in a set of L² basis functions. In the two‐body case, we recover the exact (discrete) spectrum of the CSFs for negative energies and a discretized approximation for positive ones. Besides, we make use of this method to analyze the two‐independent electron problem as a Generalized Sturmian problem. We propose a discretized version of the wave function in terms of the CSF states, and show that the problem reduces to find numerical coincidences between energy‐dependent eigencharges of the mutually independent one‐electron systems. This expansion methodology includes the continuum information which is lost in the sets used previously in the literature, and is complete when the size of the basis goes to infinity. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009