## 3D-Fourier Transform of a delta-function?

1. The problem statement, all variables and given/known data
hi
im trying to the integral int(delta(r-b)*exp(ikr)d^3r). but im not really getting anywhere.
Iīm trying to integrate over all space in spherical coordinates.
The r part is easy i just do:

delta(r-b)*exp(ikr)r^2*sin(a)*b*dr*da*db -> b^2*exp(ikb*cos(someangle??)*sin(a)*da*db

(sorry that iīm not familiar with tex :( )

I kinda need some help how to do the angular part.
My idea was that the solution should not invole the angles in any sense thatīs sure and i think that itīs some kind of trigonometric function but i got no clue how to get somewhere i have some feeling that itīs somethink link sin(bk) * normalization factor but how to get there ?

Any help would be appreciated
thanks :)
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 Recognitions: Homework Help Science Advisor The whole purpose in life of a delta function is to satisfy the condition int(delta(x-a)*f(x))=f(a). So your integral had better come out to be exp(ikb).
 but im integrating in polar coordinates not in one dimension? my intetgral (leaving out angular parts!) is int(delta(x-b) * exp(ikx))*r^2 dr isnt it ?

Recognitions:
Homework Help