What does this mean?? (Intro QM) I am on the angular momentum unit in my introductory quantum mechanics course and we had to examine the following two commutators: 1) [tex][Lx,Ly][/tex] it ends up equating to [tex]i\hbar Lz[/tex] [tex][Lx,Ly]= i\hbar Lz[/tex] [tex][Ly,Lz]= i\hbar Lx[/tex] [tex][Lz,Lx]= i\hbar Ly[/tex] Tt was concluded that no 2 components have similar eigenfunctions and no 2 components can be measured simultaneously. can anyone please explain how this is so? We were not required to take linear algebra for this course and even though I can get these answers, I do not understand what they physically mean. 2) [tex][L^2,Lx]=0 [L^2,Ly=0] [L^2,Lz]=0[/tex] And for the second commutator [tex][L^2,Lx]= 0[/tex] it was concluded that these CAN be measured simultaneously. You can know [tex]L^2[/tex] and one of its components but nothing more. Also [tex]L^2[/tex] and [tex]Lz[/tex] have similar eigenfunctions. How do you know this just from looking at commutators? Why is examining commutativity so important. What does looking at the results of the commutation relations give us physically?? any insight towards this would be greatly appreciated thanks!!