The Rapid Communications section is intended for the accelerated publication of important new results. Since manuscripts submitted to this section are given priority treatment both in the editorial once and in production, authors should explain in their submittal letter why the work justifies this special handling AR. apid Communication should be no longer than 4 printed pages and must be accompanied by an abstract. Page proofs are sent to authors.A direct numerical solution of the Schrodinger equation for quantum scattering problems is presented. The wave function for each partial wave is expanded in coupled spherical harmonics and the corresponding radial functions are expanded in a local basis set using finite-element analysis, with the appropriate scattering boundary conditions. The method is shown to give very accurate results for elastic phase shifts (S, P, D, and E) and resonance positions for electron-hydrogen scattering.PACS number(s): 34.8G.Bm Various formalisms have been developed over the years