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)
“The instincts of the ant are very unimportant, considered as the ant’s; but the moment a ray of relation is seen to extend from it to man, and the little drudge is seen to be a monitor, a little body with a mighty heart, then all its habits, even that said to be recently observed, that it never sleeps, become sublime.”
—Ralph Waldo Emerson (1803–1882)
“Here were poor streets where faded gentility essayed with scanty space and shipwrecked means to make its last feeble stand, but tax-gatherer and creditor came there as elsewhere, and the poverty that yet faintly struggled was hardly less squalid and manifest than that which had long ago submitted and given up the game.”
—Charles Dickens (1812–1870)
“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)