1. Partition functions for particle in the box:
Consider the He+ atom again with the three wave functions (that you do not need here) and energy levels, as calculated above.
a. Writhe the partition function for this system
b. Provide an expression for the relative probability of finding a population of particles in the box in the second excited state relative to the ground state at 10000K
c. What is the average energy of the system in the high temperature limit (E>> kT)
d. What is the average energy of the system in the very low temperature limit (R>> kT)?