Show that the 3 x 3 matrices G i (i = 1, 2, 3) whose elements are
Question:
Show that the 3 x 3 matrices Gi(i = 1, 2, 3) whose elements are given by
where j and k are the row and column indices, satisfy the angular-momentum commutation relations. What is the physical (or geometric) significance of the transformation matrix that connects Gi to the more usual 3 x 3 representations of the angular-momentum operator Ji with j3 taken to be diagonal? Relate your result to
under infinitesimal rotations.
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The angular momentum commutation relations for the components of angular momentum operators are given by Ji Jj iijkJk Where i j k are indices denoting ...View the full answer
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