# Density of states free electron gas

by aaaa202
Tags: density, electron, free, states
 P: 1,005 For a free electron gas the procedure for determining the density of states is as follows. 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$\pi$/L3=2$\pi$/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?