Quantum pressure of a condensate ($Q=-\frac{{\hslash }^2}{2m}\frac{{\nabla }^2\sqrt{\rho }}{\sqrt{\rho }}$)

The density-gradient contribution to the real stationary condensate equation after writing $\psi =\sqrt{\rho }{e}^{i\varphi }$. Neglecting it gives the bulk Thomas–Fermi density relation, but fails near a depleted interface or a vortex core.