where Δ Δ A 2 = ⟨ ⟨ Ψ Ψ | A 2 | Ψ Ψ ⟩ ⟩ − − ⟨ ⟨ Ψ Ψ | A | Ψ Ψ ⟩ ⟩ 2 , Δ Δ B 2 = ⟨ ⟨ Ψ Ψ | B 2 | Ψ Ψ ⟩ ⟩ − − ⟨ ⟨ Ψ Ψ | B | Ψ Ψ ⟩ ⟩ 2 , | Ψ Ψ ¯ ¯ ⟩ ⟩ is a vector that is orthogonal to the state of the system, i.e., ⟨ ⟨ Ψ Ψ | Ψ Ψ ¯ ¯ ⟩ ⟩ = 0 and one should choose the sign of ± ± i ⟨ ⟨ Ψ Ψ | [ A , B ] | Ψ Ψ ⟩ ⟩ so that this is a positive number.