The uncertainty principle (UP) comes up in engineering and physics, but it is a mathematical idea. An old text describes it as "reciprocal spreading." If $f$ is a well-behaved function, the UP might be expressed as $W(f)W(\hat{f}) \geq k$, where $k$ is some constant. If $g$ is a Gaussian, we get equality, i.e., $W(g)W(\hat{g}) = k$.
My question is this. At least in Fourier analysis, the Gaussian is sort of a minimum in the above sense. Are there any real-world problems for which this is a solution? Even in EE I don't think "optimality" of the Gaussian with respect to the UP is ever used.
Thanks for any thoughts.