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What’s the connection to Fourier Theory? My understanding was that to get a sharper PDF in position space you need a larger sum of waves, and thus a broader PDF in momentum space — and vice versa. What’s the connection to commutators/anticommutators?
this means that they are fourier conjugates, which momentum and position are
I remember seeing multiple sources (don't ask me to recall them) remarking on their surprise that Fourier didn't arrive at some version of an uncertainty principle, given how naturally it arises from the transforms.
that's because fourier was a hack
Is there any “anti-Fourier-conjugates”?
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