Saturation of harmonic-trap excited states
= Saturation of harmonic-trap excited states
At ground-relative <chemical potential> zero, the leading semiclassical excited population is $N_{\rm ex}=\zeta(3)(k_BT/\hbar\omega)^3$. Additional particles occupy the <ground state> once this capacity is reached. The continuum description requires many excited trap levels to be thermally accessible.