Читать книгу Quantum Mechanics, Volume 3 - Claude Cohen-Tannoudji - Страница 103

Let us return to the study of the time evolution of the Gross-Pitaevskii wave function and of the density variations n(r, t), without assuming as in § 1-c that the boson system stays very close to uniform equilibrium. We will show that the Gross-Pitaevskii equation can take a form similar to the hydrodynamic equation describing a fluid’s evolution. In this discussion, it is useful to normalize the Gross-Pitaevskii wave function to the particle number, as in equation (17). Equation (16) can then be written as:

(41)

where the local particle density n(r, t) is given by:

(42)