Solution
= Solution
$L_a=\varepsilon_{abc}x_bp_c$, with $[x_a,p_b]=i\hbar\delta_{ab}$ and position-position and momentum-momentum commutators zero. Expansion gives $[L_a,L_b]=i\hbar\varepsilon_{abc}L_c$ and $[L_a,p_d]=i\hbar\varepsilon_{adc}p_c$. Thus $[L_1,p_2]=i\hbar p_3\ne0$, so they are not simultaneously diagonalisable.