position and momentum are a Fourier transform pair
So anything that tightens our precision on the one
means certainty about the other value gets undone
♫♫♫
Still, I'm not sure I approve of your suggestion to use this physical property of the universe as a basis for intuition. The reasons why quantum mechanics "works" are far, far more difficult to understand, internalize, and accept than the concepts behind the DFT which only really requires an understanding of first-semester linear algebra. In other words, I expect that the set of people who understand QM at this level but do not understand the DFT is nearly empty.
If you actually meant to go the other way (use the properties of the FT/DFT to gain an understanding of QM) then I completely agree with everything you said, of course.
♫♫♫
Uncertainty is not so odd as long as we're aware
position and momentum are a Fourier transform pair
So anything that tightens our precision on the one
means certainty about the other value gets undone
♫♫♫
Still, I'm not sure I approve of your suggestion to use this physical property of the universe as a basis for intuition. The reasons why quantum mechanics "works" are far, far more difficult to understand, internalize, and accept than the concepts behind the DFT which only really requires an understanding of first-semester linear algebra. In other words, I expect that the set of people who understand QM at this level but do not understand the DFT is nearly empty.
If you actually meant to go the other way (use the properties of the FT/DFT to gain an understanding of QM) then I completely agree with everything you said, of course.