The ideal boson gas 439〈f 0 m〉=〈N〉
g. (11.6.35)
Summing both sides of eqn. (11.6.35) overmcancels the degeneracy factorgon the
right, yielding
∑m〈f 0 m〉=∑
m〈N〉
g〈f ̄ 0 〉=〈N〉, (11.6.36)where〈f ̄ 0 〉indicates that the spin degeneracy has been summed over. ForT > T 0 ,
ρλ^3 /g < R(3/2) andζis not within 1/Vof 1, implying thatζ/(1−ζ) is finite and
〈f ̄ 0 〉
〈N〉=
1
〈N〉
ζ
1 −ζ−→ 0 (11.6.37)
as〈N〉→∞. Thus, for the occupation of the ground state, we obtain
〈f ̄ 0 〉
〈N〉=
1 −(T/T 0 )^3 /^2 T < T 0
0 T > T 0
. (11.6.38)
A plot of eqn. (11.6.38) is given in Fig. 11.4.
0 1
T/T 0
0
1
<f>/< 0
N
>
Fig. 11.4Plot of eqn. (11.6.38).