Symmetry Functions of the Cube

A simple method is presented for reducing the 2J + 1 state vectors of good total angular momentum J to cubic symmetry types (basic vectors of the irreducible representations of the cubic rotation group). The cubic symmetry functions are written explicitly in terms of the eigenfunctions of Jz, Jx, and Jy, and formulas and tables which facilitate their use in obtaining eigenfunctions and energy splittings of ions in fields of cubic symmetry are presented and applied.