Читать книгу Quantum Mechanics, Volume 3 - Claude Cohen-Tannoudji - Страница 55

For bosons, the summation over nk in (7) goes from nk = 0 to infinity, which introduces a geometric series whose sum is readily computed. We therefore get:

(11)

which leads to:

(12)

For a system of free particles with spin S, confined in a box with periodic boundary conditions, we obtain, in the large volume limit:

(13)

In a general way, for fermions as well as bosons, the grand potential directly yields the pressure P, as shown in relation (61) of Appendix VI:

(14)

Using the proper derivatives with respect to the equilibrium parameters (temperature, chemical potential, volume), it also yields the other thermodynamic quantities such as the energy, the specific heats, etc.