# In quantum descriptions of atoms why are observables (which we derive from the wave function) attributed to electrons?

For example the orbital angular momentum, for the hydrogen atom. Is this the total angular momentum of the atom(electron and proton) or just the electron?

I am asking because, I am learning about how the wave function of the hydrogen atom was exited to include spin. It was necessitated because of (or something similar) the Stern-Gerlach experiment http://www.nyu.edu/classes/tuckerman/adv.chem/lectures/lecture_9/node1.html In the link above, it claims that the beam splits into two because of the magnetic moment or spin of the electrons. I understand that electron spins cancel out in atoms leaving a net spin of up or down. But I was just wondering what about the spin of the nucleus? The net spin of all the electrons would just be the spin of one electron (essentially?) How can one electron influence a whole atom. Especially Silver atoms where there a lot of electrons and a relatively large nucleus.

That's a bit badly worded. What I mean is, from the experiment the only thing you can really conclude is that the entire atom has a certain magnetic moment which causes it react to the field. What justification is given to consider the electrons magnetic moment affects the beam.

• The mass ratio of proton to electron is about $2000$. It's therefore a reasonable assumption to regards the proton to be stationary (with respect to the reference frame of the atom). – Gert Dec 29 '15 at 22:34
• There is spin-spin and spin-orbital coupling between the nucleus and the electrons, too, and the resulting spectra can be quite complex (and useful). If you take one step beyond atomic physics, the large mass difference between nuclei and electrons that Gert pointed out can be used to differentiate between rotation and vibration modes between nuclei (the electrons are following adiabatically) and electronic excitations. This greatly simplifies the theory of these systems and has given rise to the terminology. In full generality, however, the observables belong to the entire atom/molecule. – CuriousOne Dec 29 '15 at 22:57
• Right, so the spin seen in the experiments belongs to the atom? So why is the spin said to be possessed by the electron only? I don't see how the large mass difference could explain this since spin is a intrinsic property. – Shaurya Bhave Dec 30 '15 at 19:11