Variational methods for discontinuous potentials. II. Global trial functions

Abstract

For pt.I see ibid., vol.9, p.11 (1976). When conventional variational trial functions are used to solve systems such as Schrodinger's equation with discontinuous potentials, it is found that the convergence rate is very slow when compared with that for continuous potentials. In a previous paper, the authors demonstrated how this convergence rate could be improved using local variational methods (i.e. finite elements). In this paper they demonstrate the construction of trial functions for global variational methods which results in a very substantial improvement in the obtained convergence rate. The technique, which is numerically stable, is based on orthogonal polynomials with suitable core functions incorporated.