Consider a particle in a central potential with angular momentum operators \(L_x , L_y \), and\( L_z\) representing the components of the angular momentum vector \(\mathbf{L}\) . The total angular momentum operator is:
\(L^2 = L_x^2 + L_y^2 + L_z^2 \), and the corresponding eigenstates are labeled by the quantum numbers l and m . Which of the following statements is true regarding the commutation relations and the measurement of angular momentum?
\(L^2\) and \(L_z\) commute and both can be measured simultaneously.
\(L_x , L_y , and\ L_z\) can all be measured simultaneously.