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Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals of one-another, or more generally are related through Pontryagin duality. 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.

There are many types of conjugate variables, depending on the type of work a certain system is doing (or is being subjected to). Examples of canonically conjugate variables include the following:

In classical physics, the derivatives of action are conjugate variables to the quantity with respect to which one is differentiating. In quantum mechanics, these same pairs of variables are related by the Heisenberg uncertainty principle.

Canonical coordinates




This page contains text from Wikipedia, the Free Encyclopedia - http://en.wikipedia.org/wiki/Conjugate_variables

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