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Fourier transform approach to potential harmonics

✍ Scribed by John Avery; Wensheng Bian; John Loeser; Frank Antonsen

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
192 KB
Volume
63
Category
Article
ISSN
0020-7608

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✦ Synopsis

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 -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.

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