The discussion revolves around the integration of the Yukawa potential, specifically focusing on the steps involved in resolving the integral as presented in a reference. Participants are seeking clarification on the integration process, particularly the third step.
Participants generally agree on the steps involved in the integration process, but there is a lack of consensus regarding the specifics of the third step, particularly the change of variable and its implications.
There are unresolved questions regarding the treatment of differentials when changing integration variables, as well as the limits of integration, which have not been explicitly addressed in the discussion.
hello sir,ChrisVer said:1st step: go to "spherical coordinates" and integrating out the \phi... u = \cos \theta
2nd step: Integrating wrt to u, will give a difference of e^{i~something} - e^{-i~something} \propto \sin (something). In fact I wouldn't ever write it in terms of sin...
3rd step: uses that he has two integrals one with the exponential with + and the other with the exponential with - ... then changes the integration variable of the one from k to -k, and gets this result.
4th step: factorizes the denominator.
5th step and then final: solves the (complex) integral
If you want to see a step in more details, you can ask for a specific one.
Muh. Fauzi M. said:i can't get the 3rd step. is change the integration variable, change the value from k to -k in that term, including the dk -> d(-k)?