(Couldn't figure out how to make the pi symbol, but that is a pi in the denominator at the beginning. Also the limit is from 0 to inf.). I'm supposed to show this integral equals 1/(4*pi*r*r') times the delta function of (r-r').
I solved the integral and ended up with
With k ranging from 0 to infinity. Now my problem is, I'm not sure exactly how to get a delta function out of this result. I can sort of see how it might emerge on the right sided term, but I'm confused as to how to express that mathematically. Also there is apparently a pi term that comes out as well when I compare it to the expected answer. Can anyone help me?
There's probably a rule against bumping but I'm still curious about this problem and can't figure out how the delta function emerges from this integration. That should be a pi squared in the original integral so my integration is correct. Something about k ranging from 0 to infinite makes this integration look identical to the delta function. If anyone has any information they can contribute I'd appreciate it.