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Have an Integral that I can't seem to solve

  1. Sep 18, 2015 #1
    So I am working on a problem for my quantum mechanics class and I cannot seem to figure out how to solve this integral. I have looked up tables and entered it into Wolfram and it doesn't give me anything that I can work with. The integral is as follows:


    2aπ(cos(ak)+1)
    (a^2 k^2- π^2)^2

    And the bounds are from -∞ to ∞
    Any help on this would be greatly appreciated. Sorry for the crappy equation layout, I'm not sure how to use LaTeX.
     
  2. jcsd
  3. Sep 18, 2015 #2

    SteamKing

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    Is this integral perhaps:

    $$\int_{-\infty}^{\infty} \frac{2aπ\; (cos(ak)+1)}{(a^2k^2-π^2)^2}dk$$ ?
     
  4. Sep 18, 2015 #3
    yes, thak you!
     
  5. Sep 18, 2015 #4
    It is a pretty standard integral in complex analysis, and it is quite easy if you knoe how to compute integrals using residuies. If you know residues, that is a standard excersize, but if you do not no complex analysis I do not know any "elementary" ways to compute it.
     
  6. Sep 18, 2015 #5
    Yeah I was told that by the TA for the class that I should look up residue theory, never heard of it until today. Kinda surprised that our professor would put a problem that required that considering every math class I've taken has never touched the subject. Thanks for the input!
     
  7. Sep 19, 2015 #6

    SteamKing

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    Residue theory is one of the standard topics covered in calculus of complex variables. It's usually something one encounters by at least second year of undergrad ...
     
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