Integral of e^(i x v) /(x^2 + a ^2) from -Infty to Infty

[kurushishraqi]

Hi!


Solving a problem in quantum mechanics I found this integral, but I have no idea how to solve it:

$$\int_{-\infty}^{ \infty} du \frac{e^{iuv}}{u^2+a^2}$$

with $$a \in$$Reals.

If somebody have an idea, it would be appreciated. Thanks!

 

[diazona]

Hmm... are you familiar with contour integration?

 

[kurushishraqi]

Well, no. But with that info now I can solve my problem. Thanks a lot!