Spin-one spectrum of a quantum asymmetric top
= Spin-one spectrum of a quantum asymmetric top
{title2=$E=\hbar^2\{a_x+a_y,a_y+a_z,a_z+a_x\}$}
Within the $l=1$ multiplet, $|1,0\rangle$ has <energy> $\hbar^2(a_x+a_y)$. The symmetric and antisymmetric combinations of $|1,1\rangle$ and $|1,-1\rangle$ have the other two pairwise coefficient sums. Principal-axis permutation relates these energies; equality requires corresponding coefficient degeneracies rather than angular-momentum conservation alone.