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 one’s phonemes may be compared to the violinist’s 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 neighbor’s renderings indulgently, mentally rectifying the more glaring inaccuracies.”
—W.V. Quine (b. 1908)
“Sea waves are green and wet,
But up from where they die
Rise others vaster yet,
And those are brown and dry.”
—Robert Frost (1874–1963)
“The more books we read, the clearer it becomes that the true function of a writer is to produce a masterpiece and that no other task is of any consequence.”
—Cyril Connolly (1903–1974)