We might be tempted to look for simultaneous eigenfunctions of h and all three compo- nents of l. this, as we have seen in chapter 5, is only possible if all four operators com- mute with each other. to proceed we must check whether all of the operators l, l, and l, commute with each other, as well as with h. in fact, different components of the angu lar momentum do not commute with each other. for example, paying particular attention to the ordering of the operators, we get, using l-x p, (7-6a) similarly we can show that (7-6b) and (7-6c) it is true that each of the components of angular momentum commutes with l? . for ex- ample, 7-7) we can see that as a consequence of these commutation relations, only one component of l, may be chosen with h and l2 to form a simultaneously commuting set. to show this let us assume that we have a set of eigenfunctions that are simultaneous eigenfunctions of all three components of l. let us assume that and which implies that l 1n)-1,1'i̇n) and ly. ju)-illu). asa consequence of (7.6) this means that 1ju)-0.this, however implies that similarly, we can show tht aj)-o. this means that only for i.- 0 can we have simul taneous eigenfunction for all three components of the angular moncntum there i is nothing to kecp us from picking just one component of i. as part of the com- but there is nothing special about this choice muting set. conventionally the choice is we thus will deal with simaltancous cigenfunceions f and t we will denote the eigenkets by v. m) our starting point is thus the set of equations