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Dirac delta is a function given by:

We typically use it to pick specific values out of an integral:

We sometimes use shorthand and write something like this:

Where is "the delta function which is 0 everywhere but ".

Dirac delta function unit sphere:
Where are the desired where the function should be . The reason for the extra term is because of conversion to spherical coordinates.

The Dirac delta must integrate to 1 over the domain. Let's try the naïve approach without the sine (see Spherical integrals for why the term is there):

Now we add the sine term, which cancels out the other one:

#math