@@ -295,7 +295,7 @@ Also a sanity check: when the energy is close to the bottom of the band, $E = E_
1. Give an integral expression for the total energy $U$ of a 1D monatomic chain (similarly to what was done within the Debye theory). To do so, first derive the density of states from the appropriate dispersion relation given in the lecture notes.
2. Give an integral expression for the heat capacity $C$.
3. Compute the heat capacity numerically, using e.g. MatLab or Python.
3. Compute the heat capacity numerically, using e.g. Python (or Wolfram).
4. Do the same for $C$ in the Debye model and compare the two. What differences do you see?
