Constructing thermodynamic ensembles from the ground up

A very standard question in introductory statistical mechanics courses is:

The solution can be obtained almost mindlessly, by using the appropriate formulas. It goes something like this: the system’s Hamiltonian is

\[H(\boldsymbol x, \boldsymbol p)=\frac{\boldsymbol p^2}{2m} + \frac{k \boldsymbol x^2}{2}.\]

The partition function

References

1. author, “title”, journal, date.

Written on September 20th, 2025 by Alessandro Morita