Spline algorithms for continuum functions

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Abstract
Spline algorithms are described for solving the radial equation for continuum states. The Galerkin method leads to a generalized eigenvalue problem for which the eigenvalue is known so that inverse iteration can be used to determine the eigenvector. Three cases are considered: the equation whose solution is sin κr, the Coulomb problem, and the hydrogen scattering problem. Plots are presented for the first two cases that show the dependence of the error in the phase shift on spline parameters and execution time. The results for the scattering problem are compared with earlier values.

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