FOURIER TRANSFORM APPROACH TO POTENTIAL HARMONICS

摘要

Because of the high degeneracy of hyperspherical harmonics, a method is needed for selecting the most important ones for inclusion in hyperangular basis sets. Such a method was developed by M. Fabre de la Ripelle, who showed that the most important harmonics are lambda-projections of the product of the potential and a zeroth-order wave function; and he gave these the name, ''potential harmonics.'' In the present study we develop Fourier-transform-based methods for generating potential harmonics and for evaluating matrix elements between them. These methods are illustrated by a small calculation on three-body Coulomb systems with a variety of mass ratios. (C) 1997 John Wiley & Sons, Inc. [References: 33]