Δp is small enough to be considered as a differential and in one dimension dp_{x} = h/2L
where the x indicates that we are considering the positive x direction.

In 3-D there will be similar equations for the y and z directions. The volume of a state in 3-D in a cube of size L is dp_{x} dp_{y} dp_{z}, which is simply (h/2L)(h/2L)(h/2L) or h^{3}/8L^{3}.

k-space or momentum space
States are plotted on a 3-D momentum diagram (see box). The energy of each state depends on its momentum p, via E = p^{2}/2m.

The electrons in a solid will adopt the lowest possible set of p values, that is the shortest vectors in k-space. This is achieved if they all lie within a sphere known as the Fermi sphere.

After Enrico Fermi. A fermi sphere is shown in cyan on the diagram.