11. The commutator of any two angular momentum operators ( corresponding to component directions ) is non-zero. 12. In simpler terms, the total angular momentum operator characterizes how a quantum system is changed when it is rotated. 13. Where is the four-momentum that has a corresponding 4-momentum operator , and the four-potential. 14. And one of these factors is the Dirac equation ( see below ), upon inserting the energy and momentum operators . 15. But this is fundamentally the same thing, because of the close mathematical relation between rotations and angular momentum operators .) 16. The angular momentum operator plays a central role in the theory of atomic physics and other quantum problems involving rotational symmetry. 17. The term " angular momentum operator " can ( confusingly ) refer to either the total or the orbital angular momentum. 18. This may be seen from the fact that the ladder operators contain sums over the position and momentum operators of every atom. 19. There is no self-adjoint momentum operator " p " for a particle moving on a half-line. 20. In quantum mechanics, each Pauli matrix is related to an angular momentum operator that corresponds to an observable describing the isospin operator.
