The energy levels in the hydrogen atom depend only on the principal quantum number n. For a given n, all the states corresponding to ℓ ℓ = 0 , … … , n − − 1 have the same energy and are degenerate. Similarly for given values of n and ℓ, the ( 2 ℓ ℓ + 1 ) , states with m ℓ ℓ = − − ℓ ℓ , … … , ℓ ℓ are degenerate. The degree of degeneracy of the energy level E n is therefore ∑ ∑ ℓ ℓ = ⁡ ⁡ 0 n − − 1 ( 2 ℓ ℓ + 1 ) = n 2 , which is doubled if the spin degeneracy is included.