ISSN:
0020-7608
Keywords:
Computational Chemistry and Molecular Modeling
;
Atomic, Molecular and Optical Physics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
Notes:
Techniques for applying hyperspherical coordinates to the quantum-mechanical many-body problem are reviewed. An improved method is presented for evaluating matrix elements of the Hamiltonian of a system of particles. This method involves a rotation in the many-dimensional coordinate space of the system, and it can be applied not only to Coulomb potentials, but also to potentials of other types, such as, for example, the Lennard-Jones potential. It is shown that symmetry-adapted hyperspherical harmonics in the m = 3N-dimensional coordinate space of an N-particle system form a convenient basis set for the solution of the hyperangular part of the many-particle Schrödinger equation. Methods are presented for constructing hyperspherical harmonics of a type which are simultaneous eigenfunctions of Λ2, L2, and Lz, as well as being basis functions for the group of permutations of identical particles. The method presented here for coupling angular momenta by harmonic projection (without the use of Clebsch-Gordan coefficients) has broad applicability.
Additional Material:
1 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/qua.560260830
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