Computational Chemistry and Molecular Modeling
Atomic, Molecular and Optical Physics
Wiley InterScience Backfile Collection 1832-2000
Chemistry and Pharmacology
A numerical method is developed to obtain a sequence of functions converging to the eigenfunctions of the Schrödinger operator H = - ½ Δ + V(r) for V(r) = - Z/r + χ(r), where χ(r) is a continuous and bounded-from-below function for (r ∊ 0, ∞). The criterion of convergence in the convergence in the norm of the Hilbert space L2(0, ∞), which assures the accurate computation of the expected values for a symmetric operator, as we show. The method consists of solving the dirichlet problem inside a box of radius n by the Ritz method, whose convergence in the norm is proved using the compactness criterion. Using a physical argument, we show that the bounded states of the Dirichlet problem converge to those the unbounded system in the norm of L2(0, ∞) as n grows. The method is applied to the potentials V(r) = - Z/r + ari (i ≥ 0) and V(r) = - Z/r + a/(1 + rλ); in each case, we show the numerical convergence of eigenfunctions, energies, and density moments. © 1994 John Wiley & Sons, Inc.
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