In order for that to reconcile in the classical limit with Hamilton's equations of motion, [ H ^ ^ , Q ^ ^ ] must depend entirely on the appearance of P ^ ^ in the Hamiltonian and [ H ^ ^ , P ^ ^ ] must depend entirely on the appearance of Q ^ ^ in the Hamiltonian. Further, since the Hamiltonian operator depends on the (generalized) coordinate and momentum operators, it can be viewed as a functional, and we may write (using functional derivatives): [ H ^ ^ , Q ^ ^ ] = δ δ H ^ ^ δ δ P ^ ^ ⋅ ⋅ [ P ^ ^ , Q ^ ^ ] [ H ^ ^ , P ^ ^ ] = δ δ H ^ ^ δ δ Q ^ ^ ⋅ ⋅ [ Q ^ ^ , P ^ ^ ] .