PROOFS PROGRAMME

qm/que/02003

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  Let
      $$L_x =yp_z-zp_y,\ \  L_y=zp_x-xp_z, \ \ \mbox{ and } L_z=xp_y-yp_x $$  be the angular momentum operators. Prove any one of the following.
          $$ [ L_x, L_y] = i \hbar L_z $$
          $$ [ L_y, L_z] = i \hbar L_x $$
          $$ [ L_z, L_x] = i \hbar L_y $$
      Use the fundamental commutators,      \[[x,p_x]=i\hbar,\quad [y,p_y]=i\hbar,\quad [z,p_z]=i\hbar,\]        and the identities involving commutators.

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