Talk:Gaussian function

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)