Hitoshi Kitada (email@example.com)
Sun, 14 Mar 1999 09:26:41 +0900
From: Stephen P. King <firstname.lastname@example.org>
To: Robert Fung <email@example.com>
Cc: Robert Fung <Robert.Fung@citicorp.com>; Time List <firstname.lastname@example.org>
Date: Sunday, March 14, 1999 9:13 AM
Subject: [time 11] The FT of a single pulse
> I wonder if we could get this guy onboard? :) I found it on DejaNews...
Do you mean by "onboard" that we should include him in the time list? If so I
agree. Could you please take his permission for us to add him in the list?
> Re: The FT of a single pulse.
> 25 Feb 1999 00:00:00 GMT
> Eric Forgy <email@example.com>
> Center for Computational Electromagnetics
>The Heisenberg uncertainty principle is related to this question. In
>fact, the uncertainty principle is intimately tied with the Fourier
>transform. One of the fundamental properties of Fourier transforms is
>that if your pulse is "time-limited", i.e. it goes to zero outside some
>window in time, then the spectrum of the pulse cannot be "bandlimited",
>i.e. the spectrum extends to infinity.
>Translating this to uncertainty, by saying a pulse (wave function) is
>timelimited, in effect you are saying that you know with 100% certainty
>that the pulse is localized in time. This means that the uncertainty in
>frequency (energy) is infinite, i.e. the spectrum (possible energies)
>extends to infinity.
>The conclusion, pulses localized in time have infinite uncertainty in
>energy. Similarly, wave functions localized in space have infinite
>uncertainty in momentum.
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