Episode 1036
Green's function Wed, 2020Mar04 01:08 UTC Length  2:26
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With 231,051 views on Tuesday, 3 March 2020 our article of the day is Green's function.
In mathematics, a Green's function is response to the elementary impulse of an inhomogeneous linear differential operator, which is defined on a domain with specified initial or boundary conditions.
This means that if L is the linear differential operator, then
the Green's function G is the solution of the equation LG = δ, where δ is Dirac's delta function;
the solution of the initialvalue problem Ly = f is the convolution (G * f), where G is the Green's function. Through the superposition principle, given a linear ordinary differential equation (ODE), L(solution) = source, one can first solve L(green) = δs, for each s, and realizing that, since the source is a sum of delta functions, the solution is a sum of Green's functions as well, by linearity of L.
Green's functions are named after the British mathematician George Green, who first developed the concept in the 1830s. In the modern study of linear partial differential equations, Green's functions are studied largely from the point of view of fundamental solutions instead.
Under manybody theory, the term is also used in physics, specifically in quantum field theory, aerodynamics, aeroacoustics, electrodynamics, seismology and statistical field theory, to refer to various types of correlation functions, even those that do not fit the mathematical definition. In quantum field theory, Green's functions take the roles of propagators.
This recording reflects the Wikipedia text as of 01:08 UTC on Wednesday, 4 March 2020.
For the full current version of the article, see Green's function on Wikipedia.
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