Relation Between Space and Reciprocal Space
The momentum representation of a wave function is very closely related to the Fourier transform and the concept of frequency domain. Since a quantum mechanical particle has a frequency proportional to the momentum (de Broglie's equation given above), describing the particle as a sum of its momentum components is equivalent to describing it as a sum of frequency components (i.e. a Fourier transform). This becomes clear when we ask ourselves how we can transform from one representation to another.
Read more about this topic: Position Space
Famous quotes containing the words relation between, relation, space and/or reciprocal:
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—W.H. (Wystan Hugh)
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—Henry David Thoreau (1817–1862)
“No being exists or can exist which is not related to space in some way. God is everywhere, created minds are somewhere, and body is in the space that it occupies; and whatever is neither everywhere nor anywhere does not exist. And hence it follows that space is an effect arising from the first existence of being, because when any being is postulated, space is postulated.”
—Isaac Newton (1642–1727)
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—Franklin D. Roosevelt (1882–1945)