For the operator J^2, the eigenvalue is given by j(j+1), where j is the total angular momentum quantum number. In this case, j = 3/2, so the eigenvalue of J^2 is (3/2)(3/2 + 1) = 3/2 * 5/2 = 15/4.
For the operator Jz, the eigenvalue is given by m, where m is the
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