Читать книгу Quantum Mechanics, Volume 3 - Claude Cohen-Tannoudji - Страница 58

The mode j = i contribution can be expressed as:

(21)

We then get:

(22)

which, using (11), amounts to:

(23)

where the Bose-Einstein distribution function is defined as:

(24)

This distribution function gives the average population of the individual state |ui〉 with energy e. The only constraint of this population, for bosons, is to be positive. The chemical potential is always less than the lowest individual energy ek. In case this energy is zero, μ must always be negative. This avoids any divergence of the function .

Hence for bosons, the average value of any one-particle operator is obtained by inserting (23) into relation (15).