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Which Basis Is More Fundamental?

Saying that QM favors the position basis because things can be computed locally is a petitio principii, because it assumes that locality in position space is somehow more significant than locality in momentum space. You can just as easily compute things locally in momentum space. Potentials can just as easily be defined in momentum space, and it is often more convenient to do so in QFT. In fact, I can compute things more locally in momentum space than I can in position space, because I don't even need to know the infinitesimal neighborhood. The S.E. with a classical Hamiltonian in momentum space looks like , and contains no derivatives in .