Читать книгу Quantum Mechanics, Volume 3 - Claude Cohen-Tannoudji - Страница 160

The function only depends on the variational energies , since the trace of (32) may be computed in the basis {}, which yields:

(33)

We simply get an expression similar to relation (7) of Complement B_XV, obtained for an ideal gas. Since for fermions nk can only take the values 0 and 1, we get:

(34)

whereas for bosons nk varies from 0 to infinity, so that:

(35)

In both cases we can write:

(36)

with η = +1 for bosons, and η = – 1 for fermions.

Computing the entropy can be done in a similar way. As the density operator has the same form as the one describing the thermal equilibrium of an ideal gas, we can use for a system described by the formulas obtained for the entropy of a system without interactions.