- #1
Beer-monster
- 296
- 0
Okay, so I've been asked to calculate the Fermi energy of n 2D free particles of mass m, given that the density of states does not depend on energy i.e N(e) = D for E>0.
Now I know that the general recipe for this is:
[tex] n = \int{N(E).dE} = \int{D.dE} = DE [/tex]
So that the energy is [tex] E = \frac {n}{D} [/tex] and this is the right answer for the Fermi energy. I'm just not sure why I know that this energy is the Fermi energy. I know it has something to do with the fact that at T = 0 the max energy is the fermi energy, but I'm not sure how to link that to this problem?
Also does anyone know how I get from the above result to the total energy of the Fermi gas, and how this stuff relates to thermal velocity in metals?
Now I know that the general recipe for this is:
[tex] n = \int{N(E).dE} = \int{D.dE} = DE [/tex]
So that the energy is [tex] E = \frac {n}{D} [/tex] and this is the right answer for the Fermi energy. I'm just not sure why I know that this energy is the Fermi energy. I know it has something to do with the fact that at T = 0 the max energy is the fermi energy, but I'm not sure how to link that to this problem?
Also does anyone know how I get from the above result to the total energy of the Fermi gas, and how this stuff relates to thermal velocity in metals?