Free Electron Density of States question

[Master J]

I have seen thee following relation in regards to free electron waves with wavevector k :

< k | k' > = (2.pi)^3 . d( k - k') where d() is a Dirac delta function.

Why the 2.pi factor?? I can't seem to motivate it. Also, from this, it is stated that the density of states is then 1 / (2.pi)^3 ? I don't see how this relates to that factor at all?? how does one deduce that from the above?

 

[Bill_K]

This follows from the fact that the integral of exp(ikx) over all x is 2π δ(k).

 

[Master J]

Ah I see. That integral looks like a Fourier Transform?