∫ ∫ Y ℓ ℓ m ⋅ ⋅ Y ℓ ℓ ′ m ′ ∗ ∗ d Ω Ω = δ δ ℓ ℓ ℓ ℓ ′ δ δ m m ′ , ∫ ∫ Ψ Ψ ℓ ℓ m ⋅ ⋅ Ψ Ψ ℓ ℓ ′ m ′ ∗ ∗ d Ω Ω = ℓ ℓ ( ℓ ℓ + 1 ) δ δ ℓ ℓ ℓ ℓ ′ δ δ m m ′ , ∫ ∫ Φ Φ ℓ ℓ m ⋅ ⋅ Φ Φ ℓ ℓ ′ m ′ ∗ ∗ d Ω Ω = ℓ ℓ ( ℓ ℓ + 1 ) δ δ ℓ ℓ ℓ ℓ ′ δ δ m m ′ , ∫ ∫ Y ℓ ℓ m ⋅ ⋅ Ψ Ψ ℓ ℓ ′ m ′ ∗ ∗ d Ω Ω = 0 , ∫ ∫ Y ℓ ℓ m ⋅ ⋅ Φ Φ ℓ ℓ ′ m ′ ∗ ∗ d Ω Ω = 0 , ∫ ∫ Ψ Ψ ℓ ℓ m ⋅ ⋅ Φ Φ ℓ ℓ ′ m ′ ∗ ∗ d Ω Ω = 0.