3. 1d Born approximation. For 1 dimensional scattering with potential V(x), it is also possible to write the solution in the form of 2m *(x) = Aeikz + :| da'G(x,x')V(x')w*(x'), where G(x, x') is a Green's function satisfying aG(r, r') + k°G(r, x') = 6(x – x'). %3D
3. 1d Born approximation. For 1 dimensional scattering with potential V(x), it is also possible to write the solution in the form of 2m *(x) = Aeikz + :| da'G(x,x')V(x')w*(x'), where G(x, x') is a Green's function satisfying aG(r, r') + k°G(r, x') = 6(x – x'). %3D
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Question: Use the form of the Green's function in (image 2) and derive the expression for 1D Born's approximation.
Transcribed Image Text:3. 1d Born approximation.
For 1 dimensional scattering with potential V (x), it is also possible to write the solution in
the form of
6*(x) = Ae"
ikr
+
2m / da'G(x,2')V(x')st(2'),
where G(x, x') is a Green's function satisfying
ar2 G(x, x') + k²G(x, x') = 8(x – x').
Transcribed Image Text:-eik(x-a')
2ik
x > x'
e-ik(a-a') x < x'
G(2, a') =
1
2ik
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