Alternative sets of hyperspherical harmonics: Satisfying cusp conditions through frame transformations
Abstract
By extending the concept of Eulerangle rotations to more than three dimensions, we develop the systematics under rotations in higherdimensional space for a novel set of hyperspherical harmonics. Applying this formalism, we determine all pairwise Coulomb interactions in a fewbody system without recourse to multipole expansions. Our approach combines the advantages of relative coordinates with those of the hyperspherical description. In the present method, each Coulomb matrix element reduces to the "1/r" form familiar from the twobody problem. Consequently, our calculation accounts for all the cusps in the wave function whenever an interparticle separation vanishes. Unlike a truncated multipole expansion, the calculation presented here is exact. Following the systematic development of the procedure for an arbitrary number of particles, we demonstrate it explicitly with the simplest nontrivial example, the threebody system.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 April 1999
 DOI:
 10.1063/1.532857
 arXiv:
 arXiv:physics/9905053
 Bibcode:
 1999JMP....40.2162H
 Keywords:

 41.20.Cv;
 02.30.Sa;
 02.10.Cz;
 02.10.Sp;
 Electrostatics;
 Poisson and Laplace equations boundaryvalue problems;
 Functional analysis;
 Physics  Atomic and Molecular Clusters;
 Nuclear Theory
 EPrint:
 19 pages, no figures