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.
Please help me in evaluating this integral.
I'll assume that . Integrate the function round the contour consisting of (a long interval on) the real axis plus a large semicircle in the upper half-plane. The result will be equal to 2πi times the residue at the double pole at z=is.
The residue is . If I have done the calculation correctly then .
If then the answer will be the same except that you have to replace by .