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Homework Statement
I'm working on converting a single-dimension wavefunction to its momentum representation. Here is the integral I am stuck with (I've pulled out some constants):
\int\limits_{-\infty}^{\infty}\frac{e^{\frac{-ipx}{\hbar}}}{x^2+a^2}\textrm{d}x
Homework Equations
Integration by parts, x = atanθ, e^iθ = cosθ + isinθ
The Attempt at a Solution
I've tried integrating by parts, but the problem is I always get something nasty multiplied by an exponential and I can't seem to make them get along. I've also tried Euler's formula, but that doesn't seem to help me either (I end up with something like cos(tanθ)dθ after trying to make a trig substitution to get the 1/(x^2 + a^2) part to behave.
Any ideas?