✍ Scribed by E. Chacón; A. Amaya
No coin nor oath required. For personal study only.
A method proposed earlier by Aguilera, Moshinsky, and Kramer, for adapting a system of translationally invariant four-particle harmonic oscillator functions to the symmetry of the permutation group S(4), is applied to hyperspherical harmonic functions depending on three relative vectors. Except for a few cases in which diagonalization of matrices is required, the method gives closed formulas for orthonormal sets of harmonic functions with good permutational symmetry. The matrix elements of S(4) permutations with respect to the harmonic functions are obtained.
📜 SIMILAR VOLUMES
In this study we have developed the classical four-body problem using ¨w a system of hyperspherical coordinates proposed by Ohrn and Linderberg Mol. Phys. 49, Ž .x 53 1982 . Expressions are given for the canonical momenta, principal moments of inertia, total angular momentum, kinetic energy, and, fi
The exactly solvable three-body model of Crandall ef al. is used to demonstrate the effectiveness and limitations of currently popular hyperspherical-harmonic expansions.