Quantum Mechanical Addition of Angular Momenta and Spin

In this section we consider composite systems made up of several particles, each carrying orbital angular momentum decribed by spherical harmonics Y`m(θ, φ) as eigenfunctions and/or spin. Often the socalled total angular momentum, classically speaking the sum of all angular momenta and spins of the composite system, is the quantity of interest, since related operators, sums of orbital angular momentum and of spin operators of the particles, commute with the Hamiltonian of the composite system and, hence, give rise to good quantum numbers. We like to illustrate this for an example involving particle motion. Further below we will consider composite systems involving spin states.