Stern-gerlach experiment?

Question

Why does the Stern-Gerlach experiment show that the operator "measure the z component of the magnetic moment of an Ag atom" has only two eigenfunctions with eigenvalues that have the same magnitude and opposite sign?

Answer 1

Because only two states reveal themselves in the Experiment.
In Classical Mechanics we would have expected a broad band of dispersion of the Ag atoms by a Magnetic Field as the magnetic dipole of the electrons would be expected to have random orintation wrt the Magnetic Field


AND To conserve Angular Momentum we must assign Spin 1/2 to electrons.
Two states with this spin in a Magnetic Field gives us just UP and DOWN. (by analogy with the L quantum number)