quantum partition function

Given a quantum mechanical system with Hamiltonian $H\,$ and states $\left|\Psi_n\right\rangle\,$ that satisfy

$H \left|\Psi_n\right\rangle = E_n \left|\Psi_n\right\rangle\,$ ,

the quantum partition function is the quantum analogue of the partition function, and is defined to be

$Z = \sum_n g(n) e^{-\beta E_n}\,$ .

This may be rewritten as

$Z = \operatorname{tr}\, e^{-\beta H}\,$ .

The partition function is sometimes called the trace of the heat kernel.

References

↑ Bolina, O. (2002). "Trotter formula and thermodynamic limits". arXiv:physics/0202003.