We can write | ψ ψ ′ ⟩ ⟩ = V | ψ ψ ⟩ ⟩ as: | ψ ψ ′ ⟩ ⟩ = ∑ ∑ α α , γ γ = 1 χ χ ∑ ∑ i , j = 1 M λ λ α α Θ Θ α α γ γ i j λ λ γ γ | α α i j γ γ ⟩ ⟩ where Θ Θ α α γ γ i j = ∑ ∑ β β = 1 χ χ ∑ ∑ m , n = 1 M V m n i j Γ Γ α α β β [ C ] m λ λ β β Γ Γ β β γ γ [ D ] n .