Now, | Φ Φ 1 ( 0 ) ⟩ and | Φ Φ 2 ( 0 ) ⟩ are eigenstates of the Hamiltonian H 0 corresponding to different eigenvalues and as H 0 is itself Hermitian, they are orthonormal : ⟨ Φ Φ i ( 0 ) | Φ Φ j ( 0 ) ⟩ = δ δ i j