## Number operator help

I am sorry I don't know what you mean, is it like $N/V = \int (\frac{1}{(2\pi)^3}) d^3 k d^3 k' a^\{dagger} a = \int (\frac{1}{(a2\pi)^3}) d^3 k a^\{dagger} a$
 so as in the Volume cancels with the second d^3 k' term?
 N=Ʃk a+a=V/(2∏)3∫d3k a+a,V is volume.

 Tags 2nd quantisation, fermionic n operator, number operator