Читать книгу Quantum Mechanics, Volume 3 - Claude Cohen-Tannoudji - Страница 20

For bosons, we introduce the linear operator defined by:

(A-16)

As all the states of the Fock space may be obtained by a linear superposition of |n₁, n₂, .., ni, ..〉, the action of is defined in the entire space. It adds a particle to the system, which goes from a state of S(N) to a state of S(N + 1), and in particular from the vacuum to a state having one single occupied state.

Creation operators acting on the vacuum allow building occupied states. Recurrent application of (A-16), leads to:

(A-17)

Comment:

Why was the factor introduced in (A-16)? We shall see later (§ B) that, together with the factors of (A-7), it simplifies the computations.