Problems and Solutions on Thermodynamics and Statistical Mechanics

406 Problem8 d Solutions on Thermodynamics d Statistical Mechanics

2. We have o = e2DN(EF) - e2vg - EF. Let the total number of
   electrons be z, and the number density of electrons be p, then

z/L (one-dimensional)

P= { z/A (two-dimensional)

z/V (three-dimensional)

h2 2

8m L

As EF = - ("> for all the three cases, and

we have

(one-dimensional)

(two-dimensional)

(three-dimensional) ,

(one-dimensional)

(two-dimensional)

(three-dimensional).

This results differ greatly from those of the classical theory. The rea-

son is that only the electrons near the Fermi surfaces contribute to the

conductivity.

2208

(a) List and explain briefly the assumptions made in deriving the Boltz-

mann kinetic equation.

(b) The Boltzmann collision integral is usually written in the form

where fl = f(r,vI,t), fi = f(r,vh,t) and o(n) is the differential cross

section for the collision (v1,va) + (v;,~;). Derive this expression for

the collision integral and explain how the assumptions come in at various

stages.

(SVNY, Buflulo)