Partition Functions for FermiDirac and BoseEinstein particles

[mark.laidlaw19]

Homework Statement

Consider two particles, each can be in one of three quantum states, 0, e and 3e, and are at temperature T. Find the partition function if they obey Fermi Dirac and Bose Einstein statistics.

Homework Equations

The Attempt at a Solution

I have obtained solutions to both :

FD, Z = exp[-beta * e] + exp[-2 * beta * e] + exp[-4 * beta * e]

BE,Z = 1 + exp[-beta * e] + 2*exp[-3 * beta * e] + exp[-4 * beta * e] + exp[-6 * beta * e]

I have figured these out by thinking through the possible states for the particles. I'm assuming they have to be indistinguishable. I just want to confirm that my thinking has led to the correct results.

Many thanks

 

[BvU]

What expression for Z did you not provide under 2. Homework Equations ?