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

Thread starter kurushishraqi
Start date Mar 12, 2011
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Integral

AI Thread Summary

The integral in question is ∫_{-∞}^{∞} du (e^{iuv} / (u^2 + a^2)), relevant in quantum mechanics. The initial poster expressed uncertainty on how to solve it. A suggestion to use contour integration was made, which the poster was unfamiliar with. After receiving this guidance, the poster felt equipped to tackle the problem. This exchange highlights the importance of contour integration in solving complex integrals in physics.

Mar 12, 2011

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 \inReals.

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

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Mar 13, 2011

diazona

Homework Helper

Hmm... are you familiar with contour integration?

Mar 13, 2011

kurushishraqi

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

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