= Finite-box ground-energy convention in Bose condensation
{title2=$\mu\to E_0^-$}
A hard-wall cube has positive one-particle ground <energy> $E_0=3\pi^2\hbar^2/(2mL^2)$. Condensation corresponds to the absolute <chemical potential> approaching $E_0$, not zero. Shifting the <energy> reference makes the limiting <chemical potential> zero, while the exact shifted excited-state <density of states> also shifts. Keeping its bulk square-root form is a large-system approximation valid when $k_BT\gg E_0$. A periodic cube instead has zero ground <energy>.
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