Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

About Simple Poles

  1. Oct 1, 2009 #1
    In the mathematical text I've read, it says that [tex]\frac{e^{ikz}}{z^{2}+m^{2}}[/tex] has only one simple pole, that is, [tex]im[/tex], if [tex] k>0 [/tex]. Why?
    Has it got 2 simple poles, [tex] im [/tex] and [tex] -im [/tex] ?
    Last edited: Oct 1, 2009
  2. jcsd
  3. Oct 1, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You are correct. It has simple poles at [tex]im[/tex] and [tex]-im[/tex]. Either your text is wrong or perhaps there's a restriction on the domain that you didn't notice.
  4. Oct 2, 2009 #3
    It does have two simple poles at im and -im, but if k is positive the contour will be closed upwards (the contour's edges run along with x-axis, then form a half circle in the upper plane; taking the radius of the half circle to infinity, we find that this contour is exactly equal to the integral we are interested in) and the only pole enclosed will be the one at +im.

    Therefore, there is only one pole that contributes to the residue.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: About Simple Poles
  1. Simple Pole (Replies: 32)