12 = 12 + 13 + 13 show that L' commutes with each component separately (again show for L. at a minimum). Fill in the blanks to follow along with the tricks needed: [12, Lx] = [12 + 13 + 13, Lx] [12, L] = [+ [12, Lx] + [ [12, Lx] = 13 - 13 =? [12, Lx] = 12L. - LIL? [12, Lx] = 12Lx -( )Ly using info from McQuarrie 4-12. [13, La] = Ly(LyLo - LaLy) - inLyLz Now use the commutator [Ly, Lx] to show the above equation equals -inly, Lz - -ihlz, Ly Repeat the procedure for [L?, Lx] and show it equals -1 * [L?, Lx] What does this result tell you about the ability to measure the square of the total angular momentum and its components simultaneously