Look, here is how spin and orbital momentum were introduced in QM...
I am sure you know the famous Stern and Gerlach experiment. What happened there was a beam of silver atoms passing through an inhomogeneous magnetic field B, aligned in the z-direction. Now theory predicts that de force acting on the silver atoms is equal to the magnetic moment in the z-direction multiplyed by the first derivative of B with respect to x ,y and z. This immediately explains why the B-field cannot be homogenous because this force would be zero (dB/d(x,y,z) =0). In this case the magnetic moment of the atoms would just precess around the z-axis with a frequency that is called the Larmor-precession. Now, as you know from elementary electromagnetics, a little circular current is equivalent to a magnetic dipole. This implies that each atom is a magnetic dipole because it can be seen as a nucleus with an electrical circular current coming from the orbiting electrons. Please, let's not get into the discussion whether or not electrons actually orbit the nucleus because it is useless. I am giving you the justification for the reason why atoms can be seen as magnetic dipoles. If you have many atoms, you have many dipoles and if you add them all up you get the magnetization. This magnetization M is directly connected to the angular momentum L because of the above stated reasons (duality of circular current coming from the electrons and a magnetic dipole). In the Stern and Gerlach experiment, the force is thus also equal to the z-component of L multiplyed by the first derivatives of B with respect to x,y and z. These yield the three force components.
Now back to the experiment: Bohr proved that L was quantized using the results of the Franck-Hertz experiment and the famous Ballmer-spectral lines of a hydrogen atom. He found out that L=n * hbar where n needed to be an integer. Now, in our experiment, the magnetic moments (you know, the dipoles, or in other words the silver atoms) were randomly directed. Therefore, when passing through the B-field it was expected that the beam would deflect in many ways all symmetric around the z-axis. The reason for this is the fact that L_z varied between M and -M (the minimal and maximal magnetization value of the silver-atoms). However this was not observed. We observed that the bean had split up in only TWO subbeams yielding two dots on the detector screen. Basically this meant that L_z only had TWO possible values ofcourse. In QM it was proven that L² was proportional to l(l+1) and that L_z had 2l+1 possible values. l is the orbital quantumnumber. So we have from Stern and Gerlach that 2l+1 = 2 or that l = 1/2...But this s a big no no because it contradicts the fact that l needs to be an integer. This was the first result that suggested another quantumnumber was necessary. The experimental verification for the spin was the Zeemann-effect. You know, the doubling of energylevels when placed into an external magnetic field. It was back in 1924 (Stern and Gerlach was in 1921) that both Goudsmit and Uhlenbeck proposed the existence of the socalled intrinsic spin quantum number. This number had nothing to do with the current-dipole duality but it was a property of each atom on itself. All this was implemented in a theory and the final result was the total angular momentum J = LA + sa...I am sure you know of this. For silver l = 0 and s = 1/2 so that j=1/2 and therefore the degeneracy 2 (you know , of LA_z in stern and gerlach) = 2j+1 is RESPECTED for and integer l. All this thanks to spin s.
The best experimental verification of spin is the very accurate determination of the gyromagnetic factor g.
regards
marlon
