1) Consider the Hamiltonian for two spin-1/2 particles HA0 02 + e(012 - 022) = ....

 

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1) Consider the Hamiltonian for two spin-1/2 particles HA0 02 + e(012 - 022) = . (a) [5 points] show 0 02 = 01202x + . 2[01+02_+01_02+]; 0+ = (b) [5 points] What are the = 0 eigenstates and eigenvalues? The A = 0 eigenstates and eigenvalues? (1) (i) [10 points] /A small; (ii) [10 points] /X large. (c) Compute the eigenvalues of H perturbatively to lowest nontrivial order for (d) [5 points] Diagonalize H exactly and show that your answers agree with those of (c) in the appropriate limits. 1) Consider the Hamiltonian for two spin-1/2 particles HA0 02 + e(012 - 022) = . (a) [5 points] show 0 02 = 01202x + . 2[01+02_+01_02+]; 0+ = (b) [5 points] What are the = 0 eigenstates and eigenvalues? The A = 0 eigenstates and eigenvalues? (1) (i) [10 points] /A small; (ii) [10 points] /X large. (c) Compute the eigenvalues of H perturbatively to lowest nontrivial order for (d) [5 points] Diagonalize H exactly and show that your answers agree with those of (c) in the appropriate limits.

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