There is degeneracy caused from angular momentum; there is additional degeneracy caused by the oscillator potential. Consider the states | n , n ⟩ ⟩ , | n − − 1 , n − − 1 ⟩ ⟩ , | n − − 2 , n − − 2 ⟩ ⟩ , … … and apply the lowering operators C ∗ ∗ : C n − − 2 ∗ ∗ | n − − 1 , n − − 1 ⟩ ⟩ , C n − − 4 ∗ ∗ C n − − 3 ∗ ∗ | n − − 2 , n − − 2 ⟩ ⟩ , … … giving the sequence | n , n ⟩ ⟩ , | n , n − − 2 ⟩ ⟩ , | n , n − − 4 ⟩ ⟩ , … … with the same energy but with l decreasing by 2. In addition to the angular momentum degeneracy, this gives a total degeneracy of ( n + 1 ) ( n + 2 ) / 2