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January 23, 2002 Notes For Lecture 93 Form Of Green's Function ... - Wfu
Get January 23, 2002 Notes For Lecture 93 Form Of Green's Function ... - Wfu
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We have learned two important things: (i) the trace of the Green's function is a complex function which has poles on the real axis which correspond to the eigenvalues of H and (ii) at these poles the imaginary part of the Green's function (not its trace) is proportional to |ϕn⟩⟨ϕn| | ϕ n ⟩ ⟨ ϕ n | , which is a ...
Definition of the Green's Function Lu(x)=∫LG(x,y)f(y)dy=∫δ(x−y)f(y)dy=f(x).
The Green's function for any problem with a distributed source is the solution of the corresponding problem with an arbitrary unit point source. Once the Green's function is known, the solution of the original problem can be computed by integrating the product of the Green's function with the source function.
A Green's function is a solution to an inhomogenous differential equation with a delta function “driving term”. It provides a convenient method for solving more complicated inhomogenous differential equations.
Green's functions are named after the British mathematician George Green, who first developed the concept in the 1820s. In the modern study of linear partial differential equations, Green's functions are studied largely from the point of view of fundamental solutions instead.
To find the Green's function for a 2D domain D, we first find the simplest function that satisfies ∇2v = δ (r). Suppose that v (x, y) is axis-symmetric, that is, v = v (r). h is regular, ∇ 2h = 0, (ξ,η) ∈ D, G = 0 (ξ,η) ∈ C.
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