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.