ACCURATE COMPUTATION OF EIGENFUNCTIONS FOR SCHRODINGER-OPERATORS ASSOCIATED WITH COULOMB-TYPE POTENTIALS

A numerical method is developed to obtain convergence to the eigenfunc tions of the Schrodinger operators associated to singular potentials w hose asymptotic behavior is of the Coulomb type. The method consists i n solving the Dirichlet problem in a box with radius n by the Ritz met hod, whose convergence to the eigenfunctions in the norm of the Hilber t space L2(0, n) is provided. Using a physical argument, we show that the solutions of the Dirichlet problem converge to those of the unboun ded system in the norm of the Hilbert space L2(0, infinity) as n --> i nfinity. This last property guarantees the accurate computation of the expected values for a symmetric operator. The method is applied to th e hydrogen atom, Yukawa potential, and Hulten potential; in each case we show the numerical convergence of the eigenfunctions, eigenvalues, and density moments.