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## GR0877 Problem 87

PROBLEM STATEMENT: This problem is still being typed.

SOLUTION: (D) $\sigma_x \sigma_y - \sigma_y \sigma_x = \begin{pmatrix} 0 & 1\\ 1 & 0 \end{pmatrix} \begin{pmatrix} 0 & -i\\ i & 0 \end{pmatrix} - \begin{pmatrix} 0 & -i\\ i & 0 \end{pmatrix} \begin{pmatrix} 0 & 1\\ 1 & 0 \end{pmatrix} = \begin{pmatrix} i & 0\\ 0 & -i \end{pmatrix} - \begin{pmatrix} -i & 0\\ 0 & i \end{pmatrix} =$ $= 2i \begin{pmatrix} 1 & 0\\ 0 & -1 \end{pmatrix} = 2i \sigma_z$.

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$[J_x , J_y] = i\hbar J_z$ and then it’s cyclic permutations which work for all spin operators.