Problems and Solutions on Thermodynamics and Statistical Mechanics

Statistical Phyaica

Thus the number of states between n and n + dn is

1

2 -. 2rndn = rndn.

4

405

Hence

dn 4rmL2

N(E) = rn- = ~

dE h2 '

• 
  
  
  
  • 4rmA
    h2 '
  
  
  
  

where we have used

3. Motion in volume V(L3 = V).

E(n) = - h2 ("2

am L '

with n2 = n2 + ni + n: ,

where n, = 1,2,... ,nu = 1,2,... , and n, = 1,2....

The number of states between n and n + dn is

1

8

2. -. 4rn2dn = rn'dn.

Hence N(E) = nm2- dn = 4sV ($) 3'2

dE

(b) 1) The mean free time is inversely proportional to the probability of

collision, and the latter is proportional to the density of skates on the Fermi

surface (a9 T << TF, scatterings and collisions only occur near the Fermi

surface and we assume that elastic scatterings are the principal process).

Thus

1

re H __

N(EF) '

Hence