Integrals With An Imaginary Linear Term in The Argument of The Exponent
is proportional to the Fourier transform of the gaussian where is the conjugate variable of .
By again completing the square we see that the Fourier transform of a gaussian is also a gaussian, but in the conjugate variable. The larger is, the narrower the gaussian in and the wider the gaussian in . This is a demonstration of the uncertainty principle.
Famous quotes containing the words argument, term and/or imaginary:
“English! they are barbarians; they dont believe in the great God. I told him, Excuse me, Sir. We do believe in God, and in Jesus Christ too. Um, says he, and in the Pope? No. And why? This was a puzzling question in these circumstances.... I thought I would try a method of my own, and very gravely replied, Because we are too far off. A very new argument against the universal infallibility of the Pope.”
—James Boswell (17401795)
“There are other letters for the child to learn than those which Cadmus invented. The Spaniards have a good term to express this wild and dusky knolwedge, Grammatica parda, tawny grammar, a kind of mother-wit derived from that same leopard to which I have referred.”
—Henry David Thoreau (18171862)
“Where my imaginary line
Bends square in woods, an iron spine
And pile of real rocks have been founded.”
—Robert Frost (18741963)