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Problem 3 (15 points) Consider two particles with spin quantum number 31=l and sg=2 respectively. Their interaction can be described by the Hamilton operator 5' = M ii i; where it a I} . {a} E}; rewting 1-} in terms of S I ={, +1f compute the eigenvalues of it\"! and the number of degenerate states for each eigenvalue. {T points} The sysmm is in its lowest energy state when a measurement of the projection of the total angular momentum along the :-direction is performed. The measurement yields S: 2 It . (b) Determine the possible results for a subsequent measurement of .51: and the respective probabilities. (3 points]