Computing an orthonormal basis of symmetric or antisymmetric hyperspherical harmonics

Abstract

A numerical method to build an orthonormal basis of properly symmetrized hyperspherical harmonic functions is developed. As a part of it, refined algorithms for calculating the transformation coefficients between hyperspherical harmonics constructed from different sets of Jacobi vectors are derived and discussed. Moreover, an algorithm to directly determine the numbers of independent symmetric hyperspherical states (in case of bosonic systems) and antisymmetric hyperspherical-spinisospin states (in case of fermionic systems) entering the expansion of the A-body wave functions is presented. Numerical implementations for systems made with up to five bodies are reported.

Computation and analysis of bound vibrational spectra of the neon tetramer using row orthonormal hyperspherical coordinates

“…Their angles are defined with respect to a space fixed frame and do not take advantage of the isotropy of space, as Euler angles would. Furthermore, an identical particle symmetrization operation is difficult to implement in this coordinate system because it potentially changes all angular coordinates [18]. Consequently, giving up implementing permutations on the wavefunction may be preferred in some applications even if the price to pay is larger computations [19].…”