How does one arrive at this equality?

[Tac-Tics]

I'm reading about the path integral formulation.

How do you show that:

\delta(q' - q) = \frac{1}{2\pi} \int dp e^{i p (q' - q)}

with δ as the Dirac delta, q and q' as two position eigenstates, and (I'm only guessing) p as an iterator over the set of momenta.

I'm not sure the relationship between q and p that makes this work and I'm also not sure where that \frac{1}{2 \pi} factor comes from.

 

[Tac-Tics]

Ah, reading down half a page, they give the relationship:

\langle q \mid p \rangle = e^{ipq}

I believe that's what I was looking for.

(I just wish they'd put this stuff in the right order! It's hard not having a professor to bug.)

(But I'm still unsure where that 1/2pi comes from).