= Crossover from Gaussian to Thomas–Fermi condensate
{title2=$\chi=Na/a_0$}
Repulsive trapped condensates change smoothly from a nearly ideal <quantum harmonic oscillator> <ground state> for $\chi\ll1$ to a broad <Thomas–Fermi approximation for a condensate> for $\chi\gg1$. Comparing the <Gaussian interaction energy of a trapped condensate> with the total ideal <energy> gives $E_I/E_0=2\chi/(3\sqrt{2\pi})$. Thus $N\sim a_0/a$ is a crossover scale, not a sharply defined critical particle number. Total interaction <energy> must be compared with total ideal <energy>; comparing it with one oscillator quantum confuses total and per-particle scales.
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