separates in spherical coordinates for a central potential by writing ψ = R ( r ) Y ( θ, φ ), and introducing the separation constant l ( l + 1) . The resulting radial and angular equations are, respectively: The radial equation is brought to the Schr¨ odinger form by substituting: so equation (2) becomes: with the term in the brackets being the effective potential we mentioned above, equation (1). Now if we look at equation (3), the so called angular equation, we can do one more separation of variables by setting Y ( θ, φ ) = Θ( θ )Φ( φ ), then we will have the azimuthal angle equation, and the polar equation, the solutions of (5) are and we require the solutions Φ( φ ) to be single valued, i.e which dictates that m = 0 , ± 1 , ± 2 , ... . It is worth to recall that the r.h.s of (3) is the total angular momentum hermitian operator L 2 represented in spherical coordinates. In general L 2 admits integer and half integer solutions for the eigenvalue l , which is the result of the 3 Φ( φ + 2 π ) = Φ( φ ) Φ( φ ) = e imφ (7) 1 sin θ d dθ$^{(}$ sin θ d Θ dθ$^{)}$ − m 2 sin 2 θ Θ = − l ( l + 1)Θ (6) d $^{2}$Φ dφ 2 + m $^{2}$Φ = 0 (5) − ℏ 2 2 m d $^{2}$u dr 2 +$^{{}$ V ( r ) + ℏ 2 2 m l ( l + 1) r 2 } u = Eu (4) u ( r ) = rR ( r ) 1 sin θ ∂ ∂θ$^{(}$ sin θ ∂Y ∂θ$^{)}$ + 1 sin 2 θ ∂ $^{2}$Y ∂φ 2 = − l ( l + 1) Y (3) 1 R d dr$^{(}$ r $_{2}$dR dr$^{)}$ − 2 mr 2 ℏ 2 [ V ( r ) − E ] = l ( l + 1) (2)