= Thermal occupation of a quantum well
{title2=$p_1/p_0=e^{-(E_1-E_0)/(k_BT)}$}
For one nondegenerate thermalized particle, excited-state occupation relative to the <ground state> is set by the excitation gap, not by the absolute <energy> origin. In an <infinite square well> of width $L$, the first gap is $3\pi^2\hbar^2/(2mL^2)$. Predominant ground-state occupation requires this gap to be much larger than $k_BT$; an explicit tolerated occupation gives a quantitative <temperature> criterion. State <quantum degeneracy> adds its statistical weight.
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