Stdimtical Physics 267
Fig. 2.20.
Solution:
The density of states is
47rV ( 2m)3/2
h3
D(E) =
(a) If T = 0, the total number of electrons is
2
3
EF
N = l D(E)dE = -D(EF)EF.
(c) At low temperatures 1.1 >> kT,
= /,'D(E)dE + 7r2 -(kT)'D'(p) + -(kT)4D"'(p) 7T4 +...
6 3 60
Fy 87~V(2rn)~/' 3h3 p3/2 [1+ f (?,"I ,