Derive the 3D density of states for a system of electrons with the dispersion relation . Assume that there is no spin degeneracy (i.e., same conditions as was shown for 1D and 2D cases)

E=2m2k2 Density of states - Derivation (1D) N(k)=2k2L=kL Use k=22mE from E=2m2k2 N(E)=L22mE g(E)=L1dEdN(E)=2122mE1 Density of states - Derivation (2D) N(k)=k2(2L)2 Use k=22mE from E=2m2k2 N(E)=2mE2L2g(E)=L21dEdN(E)=22m