= Spherical Thomas–Fermi condensate
{title2=$R=a_0(15Na/a_0)^{1/5}$}
For repulsive <contact interactions> in a three-dimensional isotropic harmonic trap, neglecting the kinetic term in the <Gross–Pitaevskii equation> gives $n(r)=(\mu-m\omega^2r^2/2)/U_0$ inside $R=\sqrt{2\mu/(m\omega^2)}$ and zero outside. Normalization yields $N=8\pi\mu R^3/(15U_0)$, hence $\mu=(\hbar\omega/2)(15Na/a_0)^{2/5}$ and $R=a_0(15Na/a_0)^{1/5}$, with <oscillator length> $a_0=\sqrt{\hbar/(m\omega)}$. The <density> is parabolic but the <wavefunction> is its <square root>. Neglected <kinetic energy> rounds the edge and supplies a tail.
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