canonical commutation relation In physics the canonical commutation relation is the relation among the position and momentum of a point particle in one dimension where is the so called commutator of and is the imaginary unit and is the reduced Planck s constant This relation is attributed to Heisenberg and it implies his uncertainty principle Relation to classical mechanics By contrast in classical physics all observables commute and the commutator would be zero however an analogous relation exists which is obtained by replacing the commutator with the Poisson bracket and the constant with 1 This observation led Dirac to postulate that in general the quantum counterparts of classical observables should satisfy Representations According to the standard mathematical formulation of quantum mechanics quantum observables such as and should be represented as self adjoint operators on some Hilbert space