Conjugate variables: Difference between revisions

Revision as of 14:56, 1 December 2009

Revision as of 22:49, 16 December 2009

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{{forFor|conjugate variables in context of thermodynamics|Conjugate variables (thermodynamics)}}

In [[physics]], '''conjugate variables''' are pair of variables mathematically defined in such a way that they become [[Fourier transform]] [[dual (mathematics)|duals]] of one-another, or more generally are related through [[Pontryagin duality]]. The duality relations lead naturally to an uncertainty ([[Heisenberg uncertainty principle]]) relation between them. In mathematical terms, conjugate variables are part of a symplectic basis, and the uncertainty principle corresponds to the [[symplectic form]].

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* [[Position (vector)|Position]] and [[linear momentum]]: a precise definition of position leads to ambiguity of momentum, and vice versa.

* [[Angle]] (angular position) and [[angular momentum]];

* {{dnDn|Doppler}} and range: the more we know about how far away a [[radar]] target is, the less we can know about the exact velocity of approach or retreat, and vice versa. In this case, the two dimensional function of doppler and range is known as a [[radar ambiguity function]] or '''radar ambiguity diagram'''.

{{DEFAULTSORT:Conjugate Variables}}

[[Category:Classical mechanics]]

[[Category:Quantum mechanics]]

[[Category:Articles lacking sources (Erik9bot)]]

[[fr:Variables conjuguées]]