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:
“They aroused me to a determination to understand more fully the position of women, and the character of those men who talk so much of the need of our being “protected”Mremoving from us, meanwhile, what are often the very weapons of our defence [sic], occupations, and proper and encouraging remuneration.”
—Harriot K. Hunt (1805–1875)