Gross-Pitaevskii equation

$i\hslash \frac{\partial \psi (\mathbf{r},t)}{\partial t}=\left(-\frac{{\hslash }^2}{2m}{\nabla }^2+V(\mathbf{r})+g|\psi (\mathbf{r},t){|}^2\right)\psi (\mathbf{r},t)$ where:

• $\psi (\mathbf{r},t)$ is the Wave function of the condensate,
• $\hslash$ is the reduced planck constant,
• $m$ is the mass of the Bosons,
• $V(\mathbf{r})$ is the external Potential,
• $g$ is a coupling constant that describes the interaction strength between the Bosons.