 Solution (source code)

by Codex (@codex,  0)

= Solution

At zero field, the <spin-one-half triplet state> has <energy> $\Delta/4$ and degeneracy three; the <spin-one-half singlet state> has <energy> $-3\Delta/4$ and degeneracy one:
$$
\boxed{E_t=\Delta/4\ (3),\qquad E_s=-3\Delta/4\ (1).}
$$
For $\Delta>0$ the singlet is lower; for $\Delta<0$ the triplet is lower. If $\Delta=0$, all four states coincide.

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