The Angular Momentum Eigenvalue Problem (Revisited)

Abstract

So far, we have solved the angular momentum eigenvalue problem very specifically in the coordinate representation for the case of the orbital angular momentum eigenfunctions, the well-known spherical harmonics. Let us look at this problem once more from a much more general point of view, which can be taken over for anyangular momentum problem, or even more generally for any problem involving three hermitian operators with the same commutation relations as the L _x , L _y , and L _z . We want to solve the problem of finding the simultaneous eigenvalues and eigenvectors of the two (commuting) operators , and L _z .