I have a basic question that still is not clear to me. In QM, various operators are generators of something (ie. momentum is a generator of linear translations, Ang. Mom the generator of Rotations and such) Question 1: Let us look at L, or a component, say Lz. When we operate on a wavefunction with Lz it seems terminology implies we rotate our system and get a value, But that means we changed it and then get some result. However, we can't really know how we rotated the x-y axis since probability says we don't know how those axis are rotated, we know it is rotated, but not how? Is that correct logic? Seems kind of weird for lack of a better word. Q2: Then apply that to an experiment, what are you doing to the system to measure this generator of rotations? Are you applying a magnetic field to rotate the system? I think I am also missing the connection between math and application.