Читать книгу Quantum Mechanics, Volume 3 - Claude Cohen-Tannoudji - Страница 100

Still dealing with spinless bosons, we consider a uniform system, at rest, of particles contained in a cubic box of edge length L. The external potential V₁(r) is therefore zero inside the box and infinite outside. This potential may be accounted for by forcing the wave function to be zero at the walls. In many cases, it is however more convenient to use periodic boundary conditions (Complement C_XIV, § 1-c), for which the wave function of the individual lowest energy state is simply a constant in the box. We thus consider a system in its ground state, whose Gross-Pitaevskii wave function is independent of r:

(19)

with a μ value that satisfies equation (16):

(20)

where n₀ = N/L³ is the system density. Comparing this expression with relation (58) of Complement C_XV allows us to identify μ with the ground state chemical potential. We assume in this section that the interactions between the particles are repulsive (see the comment at the end of the section):

(21)