Question

Evaluate the commutator[Lx,Ly•Ly]•

Answer 1

Gives

$\begin{bmatrix} L_x& L_y.L_y \\ \end{bmatrix}$ =

$$[L_x,L_y]L_y+L_y[L_x,L_y]$$

Where

$[L_x,L_y]=2i\hbar L_z$

$[L_x,Ly.Ly]=i\hbar L_z+L_z(i\hbar)$

$[L_x,Ly.Ly]=2i\hbar L_z$