If H ^ ^ represents the Hamiltonian operator and | ψ ψ 1 ⟩ ⟩ and | ψ ψ 2 ⟩ ⟩ are two eigenstates corresponding to the same eigenvalue E, then H ^ ^ | ψ ψ 1 ⟩ ⟩ = E | ψ ψ 1 ⟩ ⟩ H ^ ^ | ψ ψ 2 ⟩ ⟩ = E | ψ ψ 2 ⟩ ⟩