- #1
Turtle492
- 20
- 0
Hi,
I'm a second year physics undergrad currently revising quantum mechanics, and I came across a phrase about angular momentum which has confused me, so I was wondering if anyone could help.
We looked at different components of angular momentum (in Cartesian) and decided that they did not commute with one another, but that the square of the magnitude (L^2) commutes with all of them, meaning 'that L^2 and one of the L components have a common set of eigenfunctions'. What I don't understand is how L^2 can have eigenfunctions in common with, Lx, Ly and Lz, but then Lz doesn't have any in common with say Ly.
I think maybe the problem is that I don't really understand what's meant by a 'common set of eigenfunctions'. What makes up a set? So far we've mainly looked at spin where the eigenfunctions form a complete, orthogonal set. Does the same happen with angular momentum?
Thanks for your help
I'm a second year physics undergrad currently revising quantum mechanics, and I came across a phrase about angular momentum which has confused me, so I was wondering if anyone could help.
We looked at different components of angular momentum (in Cartesian) and decided that they did not commute with one another, but that the square of the magnitude (L^2) commutes with all of them, meaning 'that L^2 and one of the L components have a common set of eigenfunctions'. What I don't understand is how L^2 can have eigenfunctions in common with, Lx, Ly and Lz, but then Lz doesn't have any in common with say Ly.
I think maybe the problem is that I don't really understand what's meant by a 'common set of eigenfunctions'. What makes up a set? So far we've mainly looked at spin where the eigenfunctions form a complete, orthogonal set. Does the same happen with angular momentum?
Thanks for your help