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).
Read more about this topic: Position And Momentum Space
Famous quotes containing the word position:
“One reason—perhaps the chief—of the virility of the Roosevelts is [their] very democratic spirit. They have never felt that because they were born in a good position they could put their hands in their pockets and succeed. They have felt, rather, that being born in a good position, there is no excuse for them if they did not do their duty by the community.”
—Franklin D. Roosevelt (1882–1945)