The calculation for DOS starts by counting the N allowed states at a certain k that are contained within [ k, k + d k ] inside the volume of the system. This procedure is done by differentiating the whole k-space volume Ω Ω n , k in n-dimensions at an arbitrary k, with respect to k. The volume, area or length in 3, 2 or 1-dimensional spherical k -spaces are expressed by Ω Ω n ( k ) = c n k n