The energy levels of a non-degenerate quantum system are εn = nE0, where E0 is a constant and n = 1, 2, 3, ... At a temperature T the free energy F can be expressed in terms of the average energy E by
1
E0 + kBT ln \(\frac{{\rm{E}}}{{{{\rm{E}}_{\rm{0}}}}}\)
2
E0 + 2kBT ln \(\frac{{\rm{E}}}{{{{\rm{E}}_{\rm{0}}}}}\)
3
E0 - kBT ln \(\frac{{\rm{E}}}{{{{\rm{E}}_{\rm{0}}}}}\)
4
E0 - 2kBT ln \(\frac{{\rm{E}}}{{{{\rm{E}}_{\rm{0}}}}}\)