Читать книгу Quantum Mechanics, Volume 3 - Claude Cohen-Tannoudji - Страница 66

To summarize, we can write in all cases:

(43)

with:

(44)

As shown in relation (C-19) of Chapter XV, this average value is simply the matrix element 〈1 : uk; 2 : ul1 : ui; 2 : uj〉 of the two-particle reduced density operator. To get the general expression for the average of any symmetric two-particle operator, we simply use (43) in (28). Consequently, for independent particles, the average values of all these operators are simply expressed in terms of the quantum Fermi-Dirac and Bose-Einstein distribution functions.

Complement C_XVI will show how the Wick theorem allows generalizing these results to operators dealing with any number of particles.