ACCURATE COMPUTATION OF EIGENFUNCTIONS FOR SCREENED COULOMB POTENTIALS

A numerical method is developed to obtain a sequence of functions conv erging to the eigenfunctions of the Schrodinger operator H = - 1/2 DEL TA + V(r) for V(r) = - Z/r + chi(r), where chi(r) is a continuous and bounded-from-below function for r is-an-element-of [0, infinity). The criterion of convergence is the convergence in the norm of the Hilbert space L2 (0, infinity), which assures the accurate computation of the expected values for a symmetric operator, as we show. The method cons ists of solving the Dirichlet problem inside a box of radius n by the Ritz method, whose convergence in the norm is proved using the compact ness criterion. Using a physical argument, we show that the bounded st ates of the Dirichlet problem converge to those of the unbounded syste m in the norm of L2(0, infinity) as n grows. The method is applied to the potentials V(r) = - Z/r + ar(i)(i greater-than-or-equal-to) 0) and V(r) = - Z/r + a/(1 + rlambda); in each case, we show the numerical c onvergence of eigenfunctions, energies, and density moments. (C) 1994 John Wiley & Sons, Inc.