Читать книгу Quantum Mechanics, Volume 3 - Claude Cohen-Tannoudji - Страница 143

For the term in H(t), the calculation is identical to the one we already did in § 1-b of Complement E_XV. We first add to the series of orthonormal states |θi (t)〉 with i = 1, 2, …, N other orthonormal states |θi (t)〉 with i = N + 1, N + 2, …, to obtain a complete orthonormal basis in the space of individual states. Using this basis, we can express the one-particle and two-particle operators according to relations (B-12) and (C-16) of Chapter XV. This presents no difficulty since the average values of creation and annihilation operator products are easily obtained in a Fock state (they only differ from zero if the product of operators leaves the populations of the individual states unchanged). Relations (52), (53) and (57) of Complement E_XV are still valid when the |θi〉 become time-dependent. We thus get for the average kinetic energy:

(18)

for the external potential energy:

(19)

and for the interaction energy:

(20)