Two ions 1 and 2, at fixed separation, with spin angular momentum operators S, and S,...
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Two ions 1 and 2, at fixed separation, with spin angular momentum operators S, and S₂, have the interaction Hamiltonian H = -JS₁ S₂, where Jo. The values of S₁2 and S₂2 are fixed at S₁(S₁ + 1) and S₂(S₂ + 1), respectively. Which of the following is the energy of the ground state of the system? A. O B.-JS₁S₂ C. -J[S₁(S₁+1)-S₂(S₂ + 1)] D. (J/2) [(S₁+S₂) (S₁ + S₂ + 1) - S₁(S₁+1) - S₂(S₂+1)] E. -(J/2) [(S₂(S₁ + 1) + S₂(S₂ + 1))/(S₁ + S₂) (S₁ + S₂ + 1)] Two ions 1 and 2, at fixed separation, with spin angular momentum operators S, and S₂, have the interaction Hamiltonian H = -JS₁ S₂, where Jo. The values of S₁2 and S₂2 are fixed at S₁(S₁ + 1) and S₂(S₂ + 1), respectively. Which of the following is the energy of the ground state of the system? A. O B.-JS₁S₂ C. -J[S₁(S₁+1)-S₂(S₂ + 1)] D. (J/2) [(S₁+S₂) (S₁ + S₂ + 1) - S₁(S₁+1) - S₂(S₂+1)] E. -(J/2) [(S₂(S₁ + 1) + S₂(S₂ + 1))/(S₁ + S₂) (S₁ + S₂ + 1)]
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