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Solving an indefinite integral

  1. Dec 14, 2008 #1
    1. The problem statement, all variables and given/known data

    1. The calculation of the probability of excitation of an atom originally in the
    ground state to an excited state, involves the contour integral
    INTEGRAL(-INF TO +INF) [S exp(iwt)/(t2 + s2)2dt
    Evaluate the above integral.

    2. Relevant equations



    3. The attempt at a solution
    Attempt: what i know that LAPLACE TRANSFORM OF (COS at) = s/(s2+ a2)
    Moreover this integral is looking inverse FOURIER TRANSFORM, But how to solve it. I am not getting it.
     
  2. jcsd
  3. Dec 14, 2008 #2

    CompuChip

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    Science Advisor
    Homework Helper

    Well, you mentioned the term "contour integral" and then wrote an integral over the real axis. So I guess the point is that you make it into a contour integral (close the integration by an infinitely large semi-arc in the complex plane) and use calculus of residues to evaluate it. Have you seen / done this before?

    <nitpick>By the way, it is an improper integral, but not an indefinite one.</nitpick>
     
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