Читать книгу Quantum Mechanics, Volume 3 - Claude Cohen-Tannoudji - Страница 144

We recognize in (20) the diagonal element (i = k) of the Hartree-Fock potential operator WHF(1, t) whose matrix elements have been defined in a general way by relation (58) of Complement E_XV:

(21)

We also noted in that complement E_XV that WHF (1, t) is a Hermitian operator.

It is often handy to express the Hartree-Fock potential using a partial trace:

(22)

where PN is the projector onto the subspace spanned by the N kets |θi(t)〉:

(23)

As we have seen before, this projector is actually nothing bu the one-particle reduced density operator normalized by imposing its trace to be equal to the total particle number N:

(24)

The average value of the interaction energy can then be written as:

(25)