For the hydrogenic atom, setting V ( r ) = − − B ℏ ℏ μ μ r with B = Z μ μ e 2 ℏ ℏ , a suitable equation for C l is C l = p r + i ℏ ℏ ( l + 1 ) r − − i B l + 1 with F l = G l = B 2 ( l + 1 ) 2 . There is an upper bound to the ladder operator if the energy is negative (so C l | n l max ⟩ ⟩ = 0 for some l max ), then if follows from equation (1) that E l n = − − F l / 2 μ μ = − − B 2 2 μ μ ( l max + 1 ) 2 = − − μ μ Z 2 e 4 2 ℏ ℏ 2 ( l max + 1 ) 2 , and n can be identified with l max + 1.