Canonical commutation relation

In quantum mechanics, the canonical commutation relation is the fundamental relation between canonical conjugate quantities (quantities which are related by definition such that one is the Fourier transform of another). For example, [ x ^ , p ^ x ] = i ℏ I {\displaystyle [{\hat {x}},{\hat {p}}_{x}]=i\hbar \mathbb {I} } between the position operator x and momentum operator px in the x direction of a point particle in one dimension, where [x , px] = x px − px x is the commutator of x and px , i is the imaginary unit, and ℏ is the reduced Planck constant (h/2π), and I {\displaystyle \mathbb {I} } is the unit operator.

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