How is it exactly i convert between a k-space sum an integral? Assume that we have some macroscopic solid. Periodic boundary conditions leads to kx,ky,kz = 2π/L, so each k-space state fills a volume (2π/L)3 or has a density of V/(2π)3. To then count for instance the number of state with wavevector k<k0, what do you then do? Intuitively I would multiply the volume of a cube of radius k0, but how does this translate into an integral exactly?