Video suggestions lecture_2
Here is a list of the video suggestions for the lecture 2 on the Debye model.
- Video on sound waves recap. This is basically the same as the greyed out part in the beginning of the lecture
- Video on the Debye model. First start off with the problem statement and how Debye proposed a fix for this. Clearly state that Debye used quantized sound waves (phonons). Introduce the dispersion relation and mention that phonons are bosons and thus we can use Bose Einstein statistics. To top it off, we could ask them the same questions as were asked in the lecture:
- Normal modes depend on the material's shape. What impact does this have on the heat capacity?
- Which k are possible and which are not?
- If all k are possible, shouldn't E be infinite? This nicely transitions to the next video.
- Video on periodic boundary conditions and the reciprocal space. First answer the questions above by mentioning the periodic boundary conditions. Then show the reciprocal space and its properties. Show that the periodic boundary conditions dicretize the reciprocal space.
- Video on the switch to spherical coordinates. First show that under a very large box the summation over k can be approximated as an integral over k and then show how we can use this to write the energy as an integrand over k. Then explain the spherical symmetry of the disperion relation and rewrite the integral in spherical coordinates. Afterwards substitute the dispersion relation in the equation.
- Video on the density of states. This is a very important quantity hence it deserves a video on its own
- Video on the low temperatures part.
- Heat capacity at low T and at interpolated temperatures.