Discrete Variable Representations for Singular Hamiltonians
B I. Schneider, N Nygaard
We discuss the application of the Discrete Variable Representation to Schr dinger problems which involve singular Hamiltonians. Unlike recent authors which invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto quadrature rule is used. The accuracy of the method is demonstrated by applying it to some simple problems. We emphasize that the method is equally capable of describing bound states and continuum solutions.
Journal of Physics B-Atomic Molecular and Optical Physics