Читать книгу Quantum Mechanics, Volume 3 - Claude Cohen-Tannoudji - Страница 85

The Gross-Pitaevskii equation is often written in conjunction with an approximation where the particle interaction potential has a microscopic range, very small compared to the distances over which the wave function φ(r) varies. We can then substitute:

(24)

where the constant g is called the “coupling constant”; such a potential is sometimes known as a “contact potential” or, in other contexts, a “Fermi potential”. We then get:

(25)

Whether in this form² or in its more general form (22), the equation includes a cubic term in φ(r). It may render the problem difficult to solve mathematically, but it also is the source of many interesting physical phenomena. This equation explains, for example, the existence of quantum vortices in superfluid liquid helium.