In the lecture today we used that the density of states is proportional to dk/dE.
I don’t recall having seen this before and I was wondering where it comes from.
The number of states per k interval is constant (2\pi/L in 1D not counting spin). Density of states is the number of states per energy interval. So to compute the density of states we convert the energy interval to k-interval with the proportionality coefficient dk/dE, and arrive to this conclusion.