Читать книгу Quantum Mechanics, Volume 3 - Claude Cohen-Tannoudji - Страница 61

For a two-particle symmetric operator we must use formula (C-16) of Chapter XV, which yields:

(28)

with:

(29)

As the exponential operator in the trace is diagonal in the Fock basis states |n₁, .., ni,.., nj,..〉, this trace will be non-zero on the double condition that the states i and j associated with the creation operator be exactly the same as the states k and l associated with the annihilation operators, whatever the order. In other words, to get a non-zero trace, we must have either i = l and j = k, or i = k and j = l, or both.