Читать книгу Quantum Mechanics, Volume 3 - Claude Cohen-Tannoudji - Страница 97

We assume that the ket describing the physical system of N bosons can be written using relation (7) of Complement C_XV:

(1)

but we now suppose that the individual ket |θ〉 is a function of time |θ(t)〉. The creation operator in the corresponding individual state is then time-dependent:

(2)

We will let the ket |θ(t)〉 vary arbitrarily, as long as it remains normalized at all times:

(3)

We are looking for the time variations of |θ(t)〉 that will yield for variations as close as possible to those predicted by the exact N-particle Schrodinger equation. As the one-particle potential V₁ may also be time-dependent, it will be written as V₁(t).