Re: Fourier analysis Heisenberg principle

In article <1141124721.158794.193600@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Fatou" <fatou19@xxxxxxxxxxxxx> wrote:
Am working on proving this heisenberg principle in one dimension
var(f)^2 .var((2*pi)^-0.5 fÂ)^2 > = 1/4 where f is the fourier
transform

when the mean of f, and its fourier transform equal 0
i have managed to show this. but i am trying to remove this restriction
of a 0 mean.
I have been given the hint h(x)=exp(-iax)*f(x+b) where a =mean of the
fourier transform squared, b=mean of the function squared

i have tried to prove this with no luck.
the second var is causing me problems as

h=Â(k) = intergral (on R) exp(-ikx)h(x) dx
=integral exp(-ikx)(exp(-iax)*f(x+b)) dx sub x+b=y
=exp(ib(k+a)) integral exp(-iy(k+a))f(y) dy

Im having trouble with the last line.
Sorry about the notation, could not find a "hat" symbol

<http://www.whim.org/nebula/math/uncertainty.html> contains a proof
of the Heisenberg uncertainty principle on R^n.

Rob Johnson <rob@xxxxxxxxxxxxxx>
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