Now p 4 = 4 m 2 ( H 0 + e 2 / r ) 2 E r = − − 1 2 m c 2 [ E n 2 + 2 E n e 2 ⟨ 1 r ⟩ + e 4 ⟨ 1 r 2 ⟩ ] = − − 1 2 m c 2 α α 4 [ − − 3 / ( 4 n 4 ) + 1 / n 3 ( ℓ ℓ + 1 / 2 ) ] where α α is the fine structure constant.