Conjugate variables: Difference between revisions

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

'''Conjugate variables''' are pairs of variables mathematically defined in such a way that they become [[Fourier transform]] [[dual (mathematics)|duals]] of one-another,<ref>[http://www.aip.org/history/heisenberg/p08a.htm Heisenberg – Quantum Mechanics, 1925–1927: The Uncertainty Relations]</ref><ref>[http://www.springerlink.com/content/r40472577250313r/ Some remarks on time and energy as conjugate variables]</ref> or more generally are related through [[Pontryagin duality]].<ref>[http://mathworld.wolfram.com/PontryaginDuality.html Pontryagin Duality – from Wolfram MathWorld]</ref> The duality relations lead naturally to an uncertainty in [[physics]] called the [[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]].<ref>[http://mathworld.wolfram.com/SymplecticForm.html Symplectic Form – from Wolfram MathWorld]</ref>

==Examples==