Hence, the energy levels are given by E n = − − m k 2 2 ℏ ℏ 2 n 2 , which coincides with the Rydberg formula for hydrogen-like atoms (Figure 6). The additional symmetry operators A have connected the different ℓ multiplets among themselves, for a given energy (and C 1), dictating n states at each level. In effect, they have enlarged the angular momentum group SO(3) to SO(4) / Z 2 ~ SO(3) × SO(3).