Position and Momentum Space - Unitary Equivalence Between Position and Momentum Operator

Unitary Equivalence Between Position and Momentum Operator

The r and p operators are unitarily equivalent, with the unitary operator being given explicitly by the Fourier transform. Thus they have the same spectrum. In physical language, p acting on momentum space wave functions is the same as r acting on position space wave functions (under the image of the Fourier transform).