Efficient boundary basis functions for time-independent quantum scattering calculations

Novel parametrically energy-dependent boundary functions, F, combined with a finite L-2 basis set, permit accurate and efficient calculation of scattering wavefunctions for many energies. Both accuracy and efficiency are achieved simultaneously because all the necessary integrals are energy-independent and also certain functionals, (H-E)\F], in the Schrodinger equation are allowed to satisfy desirable boundary conditions. In addition, slight modification of the Schrodinger equation in the boundary region is shown to be useful for improving the numerical accuracy when a cutoff-radius-truncated basis set is used. The advantages of the present approaches are demonstrated for the one-dimensional Eckart barrier problem.