FIG. 1.

(color online) Structure of the three tangent component operators t̂^z, t̂⁺, and t̂⁻ in {|l, m〉} space for the case l,l′ ≤ 3 (ignoring the n-dependence). For matrix t̂^z, only matrix elements along the main diagonal blocks are possibly non-zero (purple or dark gray); all other matrix elements are zero. For matrix t̂⁺ (t̂⁻, only matrix elements in the lower (upper) next-to-diagonal blocks are possibly non-zero (orange or light gray); all other matrix elements are zero.