Conjugate variables: Difference between revisions

Revision as of 05:35, 28 September 2006

Revision as of 19:38, 26 December 2006

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Examples of canonically conjugate variables include the following:

* Time and frequency: the longer a musical note is sustained, the more preciseprecisely we know its frequency (but it spans more time). Conversely, a very short musical note becomes just a click, and so one can't know its frequency very accurately.

* Position and momentum: precise measurements of position lead to ambiguity of momentum, and vice versa.

* [[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'''.