This site gives you a qualitative feel for how the Fourier transform A(k) of a function f(x) varies (1) as the wave number k0 of f(x) varies and (2) as the width w of f(x) varies. (For a brief review of the meaning of the Fourier transform and a quantitative example, click here.) Once you have mastered the qualitative relationships, try the challenge. Note that Quicktime is required to view all animations.
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The Fourier transform and its inverse are defined as follows:  Click on a function f(x)
to the left and watch how its Fourier transform A(k)
behaves as the function's width w
or approximate wave number k0
is varied. Two
functions can be varied only in k0,
two only in w, and two in
both. Pay particular attention to where the "spikes" are, how wide they
are, and how many there are, keeping in mind the Euler formulas, given
below.
Note that functions whose widths
change also vary inversely in height. Were such a function to be
related to the probability of finding a particle, it would have to get
taller - meaning a greater probability per unit length - as it gets
narrower.
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