For a free electron gas the procedure for determining the density of states is as follows.(adsbygoogle = window.adsbygoogle || []).push({});

Apply periodic boundary conditions to the free electron waves over a cube of side L. This gives us that there is one state per volume 2[itex]\pi[/itex]/L^{3}=2[itex]\pi[/itex]/V

And from there we can find the number of states at a given energy E by multiplying by the volume of a sphere at E in k space.

One big problem with this is however: Why do we assume that material is necessarily a cube? What if we worked with a ball of metal?

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# Density of states free electron gas

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