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===Quantum theory===
In [[quantum mechanics]], conjugate variables are realized as pairs of observables whose operators do not commute. In conventional terminology, they are said to be ''incompatible observables''. Consider, as an example, the measurable quantities given by position <math> \left (x \right) </math> and momentum <math> \left (p \right) </math>. In the quantum mechanical formalism, the two observables <math> x </math> and <math> p </math> correspond to operators <math> \widehat{x} </math> and <math> \widehat{p} </math>, which necessarily satisfy the [[canonical commutation relation]]:
: <math>[\widehat{x},\widehat{p\,}]=\widehat{x}\widehat{p\,}-\widehat{p\,}\widehat{x}=i \hbar</math>
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