Answered: G(x, x')+kG(x, a') = 8(x – x') -- Dx² | bartleby

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For 1 dimensional scattering with potential V (x), it is also possible to write the solution in the form of: (see image 1).

where G(x, x') is a Green's function satisfying: (see image 2).

Question: Find the analytical form of the Green's function and then use it to derive the expression for 1D Born's approximation.

2m
+ (x) = Aeika +
dx'G(x, x')V(x')¼+(x'),

Ən2 G(x, x') + k²G(x, x') = 8(x – x')
-
Əx?

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