The second stronger uncertainty relation is given by σ σ A 2 + σ σ B 2 ≥ ≥ 1 2 | ⟨ ⟨ Ψ Ψ ¯ ¯ A + B ∣ ∣ ( A + B ) ∣ ∣ Ψ Ψ ⟩ ⟩ | 2 where | Ψ Ψ ¯ ¯ A + B ⟩ ⟩ is a state orthogonal to | Ψ Ψ ⟩ ⟩ . The form of | Ψ Ψ ¯ ¯ A + B ⟩ ⟩ implies that the right-hand side of the new uncertainty relation is nonzero unless | Ψ Ψ ⟩ ⟩ is an eigenstate of ( A + B ) . One may note that | Ψ Ψ ⟩ ⟩ can be an eigenstate of ( A + B ) without being an eigenstate of either A or B . However, when | Ψ Ψ ⟩ ⟩ is an eigenstate of one of the two observables the Heisenberg–Schrödinger uncertainty relation becomes trivial. But the lower bound in the new relation is nonzero unless | Ψ Ψ ⟩ ⟩ is an eigenstate of both.