Discrete Green's Function
The Green's function of the discrete Schrödinger operator is given in the resolvent formalism by
where is understood to be the Kronecker delta function on the graph: ; that is, it equals 1 if v=w and 0 otherwise.
For fixed and a complex number, the Green's function considered to be a function of v is the unique solution to
Read more about this topic: Discrete Laplace Operator
Famous quotes containing the words discrete, green and/or function:
“The mastery of ones phonemes may be compared to the violinists mastery of fingering. The violin string lends itself to a continuous gradation of tones, but the musician learns the discrete intervals at which to stop the string in order to play the conventional notes. We sound our phonemes like poor violinists, approximating each time to a fancied norm, and we receive our neighbors renderings indulgently, mentally rectifying the more glaring inaccuracies.”
—W.V. Quine (b. 1908)
“I passed a tomb among green shades
Where seven anemones with down-dropped heads
Wept tears of dew upon the stone beneath.”
—Unknown. The Thousand and One Nights.
AWP. Anthology of World Poetry, An. Mark Van Doren, ed. (Rev. and enl. Ed., 1936)
“No one, however powerful and successful, can function as an adult if his parents are not satisfied with him.”
—Frank Pittman (20th century)