Conjugate variables: Difference between revisions

Revision as of 02:51, 31 May 2006

Revision as of 16:35, 2 June 2006

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In [[physics]], especially in [[quantum mechanics]], '''conjugate variables''' are pairs of variables that share an [[uncertainty principle|uncertainty relation]]. The terminology comes from classical [[Hamiltonian mechanics]], but also appears in [[quantum mechanics]] and engineering.

Examples of canonically conjugate variables include the following:

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A pair of conjugate variables are often [[Fourier transform]] duals of one-another, or more generally are related through [[Pontryagin duality]]. The duality relations lead naturally to an uncertainty relation between them.

In [[quantum mechanics]], the term denotes a pair of [[observable]]s whose [[operator]]s do not commute.

A more precise [[mathematical]] definition, in the context of [[Hamiltonian mechanics]], is given in the article [[canonical coordinates]].