Quantum statistical mechanics: Return of the simple harmonic oscillator
The energy levels of a quantum SHO are given by
1. Calculate the QM partition function.
2. Calculate the probability that a measurement of the energy will find the QM SHO in the n-th eigenstate.
3. Calculate the average energy.
4. Calculate the specific heat.
5. Calculate the high-temperature limit of the specific heat.
6. Calculate the leading term in a low-temperature expansion of the specific heat. (You should be able to figure out what a good quantity to expand in would be.)