= Two spin-one-half fermions on a ring
{title2=$E=\hbar^2(l_1^2+l_2^2)/(2mR^2)$}
For free <fermions> on a ring, each one-particle orbital has integer <angular momentum> label $l$ and two <spin> states. Two particles occupy the $l=0$ orbital in a unique <singlet state> at zero kinetic <energy>. At the next distinct <energy> $\hbar^2/(2mR^2)$, orbitals $0,+1$ or $0,-1$ can be combined with one <singlet state> or three <triplet state> <spin> states, giving total <quantum degeneracy> eight. The lowest <triplet state> has six states and its antisymmetric spatial factor vanishes when the particles coincide.
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