Additionally, let's work on density of states as a function of energy. So far we have calculated the energy of a bunch of states (one band) as a function of q. Can we turn that into a density of states as a function of energy?
To provide ourselves a concrete goal, let's work toward calculating the specific heat* of a 1D crystal with a band of the states we just calculated that is:
1) full
2) half full
*The specific heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius... (i googled it)
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