Why do we calculate the density of states using k-space?

[11thHeaven]

In statistical physics the calculation to obtain the density of states function seems to involve an integral over an eighth of a sphere in k-space. But why do we bother moving from n-space to k-space, if there's a linear relation between n and k i.e. n = (L/π)k ? Why don't we just integrate over an eighth of a sphere in n-space?

 

[jambaugh]

Could you be a bit more specific? By k-space do you mean momentum space? By n-space what do you mean then? q-space as in coordinate space? Are you talking classical statistical mechanics or quantum or both?