= Thomas–Fermi approximation for a condensate
{c}
Neglecting density-gradient <kinetic energy> in the stationary <Gross–Pitaevskii equation> gives $n=(\mu-V)_+/g$ for repulsive interactions. For a radial harmonic trap $V=m\omega_r^2r^2/2$, this is $n=n_0(1-r^2/R_r^2)_+$ with $R_r=\sqrt{2gn_0/(m\omega_r^2)}$. Hard boundaries can truncate this natural support. The approximation fails in vortex cores and boundary healing regions and requires a cloud much larger than its <healing length>.
Back to article page
