Hi Prof, I think DOS derivation would be clearer if done via using the octant with N=4/3pi (n^2) x 2 pin x 1/8octant with n= no of available energy states where E=pi^2h-bar^2n^2/2mL^2. Therefore, DOS=dN/dE proportional to C E^1/2. For DOS (k) = dN/dE * dE/dk = dN/dk , using E=h-bar^2k^2/2mL^2. This also factors the volume term out clearly with g(E)/V or g(k)/V
Hi Prof, I think DOS derivation would be clearer if done via using the octant with N=4/3pi (n^2) x 2 pin x 1/8octant with n= no of available energy states where E=pi^2h-bar^2n^2/2mL^2. Therefore, DOS=dN/dE proportional to C E^1/2. For DOS (k) = dN/dE * dE/dk = dN/dk , using E=h-bar^2k^2/2mL^2. This also factors the volume term out clearly with g(E)/V or g(k)/V
Very clear explanation