----- Original Message ---- From: Mike Stay <metaweta@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Monday, September 24, 2007 9:00:01 AM Subject: Re: [math-fun] Compute a Function From its Fourier Series? On 9/23/07, mcintosh@servidor.unam.mx <mcintosh@servidor.unam.mx> wrote:
2) The variance (or better, the standard deviation) of a function is inverse to the variance of its Fourier Transform. Thus, many large coefficients are needed to confine a function to a small region and conversely.
Which is a general form of Heisenberg's uncertainty principle. -- Mike Stay metaweta@gmail.com http://math.ucr.edu/~mike It is not correct to refer to this as "Heisenberg's" uncertainty principle. Heisenberg's uncertainty relates the variances of position and momentum. In quantum mechanics there is a connection between momentum and spatial frequency, and so the Fourier uncertainty principle can then be applied. The Heisenberg principle is exclusively quantun mechanical in nature. A classical electromagentic pulse has an exactly calculable momentum and an exactly calculable center of mass position. This is true because the energy density (E^2 + B^2) and momentum density (E x H) depend only on the fields, and not on the frequency or wavelength. Gene ____________________________________________________________________________________ Fussy? Opinionated? Impossible to please? Perfect. Join Yahoo!'s user panel and lay it on us. http://surveylink.yahoo.com/gmrs/yahoo_panel_invite.asp?a=7