Time reversal behavior of solutions to crystal spin Hamiltonian

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Q: [1] pr 4.12

Solve the spin 1 Hamiltonian \begin{equation}\label{eqn:crystalSpinHamiltonianTimeReversal:20} H = A S_z^2 + B(S_x^2 – S_y^2). \end{equation}

Is this Hamiltonian invariant under time reversal?

How do the eigenkets change under time reversal?

A:

In spinMatrices.nb the matrix representation of the Hamiltonian is found to be \be…