Читать книгу Quantum Mechanics, Volume 3 - Claude Cohen-Tannoudji - Страница 54

For fermions, as nk can only take the values 0 or 1 (two identical fermions never occupy the same individual state), we get:

(8)

and:

(9)

The index k must be summed over all the individual states. In case these states are also labeled by orbital and spin subscripts, these must also be included in the summation. Let us consider for example particles having a spin S and contained in a box of volume with periodic boundary conditions. The individual stationary states may be written as |k, ν〉, where k obeys the periodic boundary conditions (Complement C_XIV, § 1-c) and the subscript ν takes (2S + 1) values. Assuming the particles to be free in the box (no spin Hamiltonian), each ν value yields the same contribution to Φ_fermions; in the large volume limit, expression (9) then becomes:

(10)