The perturbation Hamiltonian due to relativistic correction is given by H r = − − p 4 / 8 m 3 c 2 where p is the momentum operator and m is the mass of the electron. The first-order relativistic energy correction in the | n l m ⟩ ⟩ basis is given by E r = ( − − 1 / 8 m 3 c 2 ) ⟨ n ℓ ℓ m | p 4 | n ℓ ℓ m ⟩