Consider a spin-1 particle with Hamiltonian Ĥ = AS² + B(Ŝ² − S²). Assume B < A, treat the second term as a perturbation, and calculate the unperturbed energies and their first-order corrections using perturbation theory. Be careful of the degen- eracy. Compare your perturbative results with the exact eigenvalues.

Consider a spin-1 particle with Hamiltonian Ĥ = AS² + B(Ŝ² − S²). Assume B < A, treat the second term as a perturbation, and calculate the unperturbed energies and their first-order corrections using perturbation theory. Be careful of the degen- eracy. Compare your perturbative results with the exact eigenvalues.