**Stephen P. King** (*stephenk1@home.com*)

*Sat, 13 Mar 1999 18:06:20 -0500*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Hitoshi Kitada: "[time 12] [time 11] The FT of a single pulse"**Previous message:**Hitoshi Kitada: "[time 10] Re: [time 9] Re: [time 7] Re: Gravitational Aharonov-Bohm Effect"

Dear Robert,

I wonder if we could get this guy onboard? :) I found it on DejaNews...

Later,

Stephen

Subject:

Re: The FT of a single pulse.

Date:

25 Feb 1999 00:00:00 GMT

From:

Eric Forgy <ericf@uiuc.edu>

Organization:

Center for Computational Electromagnetics

Newsgroups:

sci.physics.research

References:

1

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.

Eric

**Next message:**Hitoshi Kitada: "[time 12] [time 11] The FT of a single pulse"**Previous message:**Hitoshi Kitada: "[time 10] Re: [time 9] Re: [time 7] Re: Gravitational Aharonov-Bohm Effect"

*
This archive was generated by hypermail 2.0b3
on Sat Oct 16 1999 - 00:29:44 JST
*