Take the tour ×  I am reading about the total, orbital and spin
angular momentum, and I am not clear as to what these generators
actually do after exponentiating.  Could you give me a physical
picture of what happens to the quantum set, after being acted
upon by the operator obtained after exponentiating these?  For
example does the total angular momentum rotate the ket in a
circle, about the normal? What about the other two?
share|improve this question add comment  2 Answers  up vote 1
down vote accepted  Angular momenta are sets of three operators
$\{\hat{L}_{i}\}$ such that
$$[\hat{L}_i,\hat{L}_j]=i\hbar\epsilon_{ijk}\hat{L}_{k} $$
where $\epsilon_{ijk}$ is the Levi-Civita symbol. Orbital
angular momentum and spin are angular momenta because they
satisfy that commutation relation. (That commutator can be
derived if you define
$\vec{L}=\hat{\vec{r}}\times\hat{\vec{p}}$, a formal vector
product between vector operators)  As in classical physics,
angular momentum is useful when you have spherical symmetry.