Читать книгу Quantum Mechanics, Volume 3 - Claude Cohen-Tannoudji - Страница 79

Let us choose an arbitrary normalized quantum state |θ〉:

(6)

and call the associated creation operator. The N-particle variational kets we consider are defined by the family of all the kets that can be written as:

(7)

where |θ〉 can vary, only constrained by (6). Consider a basis {|θ_k〉} of the individual state space whose first vector is |θ₁〉 = |θ〉. Relation (A-17) of Chapter XV shows that this ket is simply a Fock state whose only non-zero occupation number is the first one:

(8)

An assembly of bosons that occupy the same individual state is called a “Bose-Einstein condensate”.

Relation (8) shows that the kets are normalized to 1. We are going to vary |θ〉, and therefore , so as to minimize the average energy:

(9)