Читать книгу Quantum Mechanics, Volume 3 - Claude Cohen-Tannoudji - Страница 86

Rather than normalizing the wave function φ(r) to 1 in the entire space, one sometimes chooses a normalization taking into account the particle number by setting:

(26)

This amounts to multiplying by the wave function we have used until now. At each point r of space, the particle (numerical) density n(r) is then given by:

(27)

With this normalization, the factor (N — 1) in (25) is replaced by (N — 1)/N, which can generally be taken equal to 1 for large N. The Gross-Pitaevskii equation then becomes:

(28)

As already mentioned, we shall see in § 4-a that μ is simply the chemical potential.