| > Why is the fourier transform of position equal to momentum? That comes out of the way you get the probability distribution of the position and the probability distribution of the momentum out of the wave function. If you do the math, then one turns out to be the fourier transformation of the either. (And of course the article skipped over this, because it needs quite a bit of math). Of course this then begs the question why there are wave functions, and why you get the position and momentum from the wave function in that particular way. And I guess the only answer I have to that is "that's how quantum mechanics works, and it matches what we observe". > More generally, why would the fourier transform of an observable be another observable? Again, that comes out of how you calculate particular observables from the wave function. Like above, if you do this for the energy probability distribution and the time probability distribution, they turn out to be related. And it's not the case for any observables you can compute. For example, the energy and position are NOT fourier transforms of each other. |