... for the fact that the orbital angular momentum weight is NOT a semi)integer positive number, but an integer. Is there such a reason...? I've never seen it in some book. I know there are other reasons for which we conclude that "l" MUST be an integer, see Sakurai's thoughts attached. However, orbital angular momentum is a type of angular momentum, the latter which, at quantum level, is the self-adjoint generator of the unitary group representations of the rotation symmetry group [itex] SO(3) [/itex]. So there has to be some group-theoretical reason for which "l" must be an integer and NOT a semi-integer, soe other that Sturm-Liouville theory of PDE-s, etc...(see Sakurai) Daniel.