Talk:Gaussian function
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Do we mean to say that
- gaussian functions are eigenfunctions of the Fourier transform,
or that
- eigenfunctions of the Fourier transform are gaussian functions
or neither? -- Miguel
Not all eigenfunctions of the Fourier transform are Gaussian. See Hermite polynomials. Michael Hardy 15:10, 30 Aug 2003 (UTC)
maximum entropy
Could someone add something about Gaussian functions being the ones with maximum entropy? I think this can also be related to the Heisenberg uncertainty principle since momentum and position are canonical conjugate variables.
- This article links to normal distribution, which I suspect already gives that information. For non-normalized Gaussian functions, I'm not sure at this moment what the maximum-entropy statement would say. Michael Hardy 23:46, 27 Feb 2005 (UTC)
image
are they all the same bell-shape? if so, let's get a picture! - Omegatron 17:51, Mar 15, 2005 (UTC)