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1. Consider the dispersion relation (1.94), which is used to model non-parabolicity in the conduction band of GaAs. Estimate the form of the density of states at small and at large energies. What happens to the velocity in these two limits?

2. Show that the density of states for free electrons in two dimensions (the simplest case) is

(Again, the result is more complicated for a realistic dispersion relation, with further singularities inside the band.)

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