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 And Momentum Space
Famous quotes containing the words relation between, relation, space and/or reciprocal:
“There is a relation between the hours of our life and the centuries of time. As the air I breathe is drawn from the great repositories of nature, as the light on my book is yielded by a star a hundred millions of miles distant, as the poise of my body depends on the equilibrium of centrifugal and centripetal forces, so the hours should be instructed by the ages and the ages explained by the hours.”
—Ralph Waldo Emerson (1803–1882)
“Skepticism is unbelief in cause and effect. A man does not see, that, as he eats, so he thinks: as he deals, so he is, and so he appears; he does not see that his son is the son of his thoughts and of his actions; that fortunes are not exceptions but fruits; that relation and connection are not somewhere and sometimes, but everywhere and always; no miscellany, no exemption, no anomaly,—but method, and an even web; and what comes out, that was put in.”
—Ralph Waldo Emerson (1803–1882)
“Time in his little cinema of the heart
Giving a première to Hate and Pain;
And Space urbanely keeping us apart.”
—Philip Larkin (1922–1986)
“Parenting is a profoundly reciprocal process: we, the shapers of our children’s lives, are also being shaped. As we struggle to be parents, we are forced to encounter ourselves; and if we are willing to look at what is happening between us and our children, we may learn how we came to be who we are.”
—Augustus Y. Napier (20th century)