Fourier transform and uncertainty principle

Fourier transform and uncertainty principle 

We mostly learn uncertainty principle in quantum mechanics. But in Fourier transform, the meaning of uncertainty principle is much more intuitive. The multiplication of standard deviations in time space and in frequency space is larger than a constant.

We often think the uncertainty principle is a property in quantum mechanics. But it is really a general property on measurement errors in any probability space and its conjugate space.

On an abstract level, many agree that the methods from quantum mechanics are general. But many are hesitant to apply the methods from quantum mechanics, such as Feynman-Kac formula, to broader areas, such as economics.