Читать книгу Quantum Mechanics, Volume 3 - Claude Cohen-Tannoudji - Страница 141

If the Hamiltonian H is time-independent, one can look for time-independent kets to make the functional S stationary. The function to be integrated in the definition of the functional S also becomes time-independent, and we can write S as:

(17)

Since the two times t₀ and t₁ are fixed, the stationarity of S is equivalent to that of the diagonal matrix element of the Hamiltonian . We find again the stationarity condition of the time-independent variational method (Complement E_XI), which appears as a particular case of the more general method of the time-dependent variations. Consequently, it is not surprising that the Hartree-Fock methods, time-dependent or not, lead to the same Hartree-Fock potential, as we now show.