In this problem we will consider chemical potential (T) for fermions and bosons.

Question

In this problem we will consider chemical potential (T) for fermions and bosons.

a) In the case of fermions at zero temperature we found in the class that (0) = F =(32)2/3(hbar2/m)*n2/3 where n is particle density. Now at finite but small temperature T F find (T) to the leading order in T/F 1.

b) In the case of bosons (T) is zero at temperatures below T0. Consider now T larger than T0 but just slightly, namely T T0 T0. Find how chemical potential approaches zero as T approaches T0. Express our answer in terms of N N0(T ) where N0(T ) is the number of boson occupying the lowest energy state. Note that is negative and approaches zero from below.

Explanation / Answer

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