Starting with Kennard's derivation of position-momentum uncertainty, Howard Percy Robertson developed a formulation for arbitrary Hermitian operator operators O ^ ^ expressed in terms of their standard deviation σ σ O = ⟨ ⟨ O ^ ^ 2 ⟩ ⟩ − − ⟨ ⟨ O ^ ^ ⟩ ⟩ 2 , where the brackets ⟨ ⟨ O ⟩ ⟩ indicate an expectation value. For a pair of operators A ^ ^ and B ^ ^ , define their commutator as [ A ^ ^ , B ^ ^ ] = A ^ ^ B ^ ^ − − B ^ ^ A ^ ^ ,