I recently read a question on fermi's golden rule posted here:
Fermi's Golden Rule and Density of States
However, I do not really know how you would go about obtaining a value for the density of states? Classmates are suggesting that it is the number of electrons allowed in an energy level but we are unsure which energy levels we should consider if this were true.
The density of states $D(E)$ is the number of states at a given energy $E$. For a finite system, this is rather boring, because there are only states at discrete energy levels - that's what you're talking about. Assume a system with the energy levels $E_1$,$E_2$,$E_3$,$E_4$, then the density of states is
$D(E)=\sum_{i=0}^4\delta(E-E_i)$.
This expression says that there is one state at the energies $E_i$, but none elsewhere. For continuous systems, this is more interesting. The number of states can differ between energies, e.g. in Silicon: http://nanohub.org/resource_files/2011/11/12603/slides/026.01.jpg. This is particularly important because the gap in this picture between 0 and approx. 1 eV is what makes silicon a semiconductor.
