Question: The Hamiltonian for a spin 1 system is given by H = AS 2 z + B (S 2 x S 2 v ).

The Hamiltonian for a spin 1 system is given by

H = AS²_z + B (S²_x – S²_v).

Solve this problem exactly to find the normalized energy eigenstates and eigenvalues. (A spin-dependent Hamiltonian of this kind actually appears in crystal physics. It this Hamiltonian invariant under time reversal? How do the normalized eigenstates you obtained transform under time reversal?

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