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## pGR0877 Problem 95

PROBLEM STATEMENT: This problem is still being typed.

SOLUTION: (D) As you can check for yourself $[J_x, J_y] = i \hbar J_z$ (the other two commutation relations can be obtain be cyclic permutation of the indexes $x \to y$, $y \to z$, $z \to x$; note also that I do not use the sign $\hat{}$ for the operators). Using a sweet relation one must remember (or derive if needed) on the PGRE $[AB,C] = A[B,C] + [A,C]B$ one has $[J_xJ_y, J_x] = J_x[J_y, J_x] + [J_x, J_x]J_y = -i \hbar J_xJ_z$ (here I’ve used the property that any operator commutes with itself).

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$[AB,C] = ABC - CAB$
$[AB,C] = ABC - CAB + ACB - ACB = ABC - ACB + ACB - CAB = A(BC - CB) + (AC - CA)B = A[B,C] + [A,C]B$