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Hakkinen
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Homework Statement
Given a linear operator [itex]L=\frac{d^3}{dx^3}-1[/itex], show that the Fourier transform of the Green's function is [itex]\tilde{G}(k)=\frac{i}{k^3-i}[/itex] and find the three complex poles. Use the Cauchy integral theorem to compute G(x) for x < 0 and x > 0.
Homework Equations
The Attempt at a Solution
I found the Fourier transform of the Green's function and solved for the three complex roots. I'm having trouble setting up and carrying out the contour integration though. I think that you should be able to write (k^3 - i ) somehow in terms of the roots, then break the contour integral up into three separate integrals around each contour with terms like (k - ...)(k - ...)(k - ...) in each denominator?
Any assistance is greatly appreciated!