Applicability of WKB descriptions

Figure: Regions of Applicability of WKB Descriptions.

[width=.6]fig2.eps

In this section we will investigate the applicability of the above theory. Let us consider a condensate which is a solution of the eigenvalue problem $\partial_{t}\psi_{0} = -i \Omega \psi_{0}$. Therefore, the GP equation () becomes

$$\Omega \psi_{0}+\triangle\psi_{0}-\varrho\psi_{0} - U\psi_{0} = 0.$$ (15)