Is the spin magnetic moment of a fundamental particle like an electron always aligned along the direction of the spin angular momentum (meaning that the magnetic moment and the spin operators have the same eigenstates)? Is it true for composite particles like protons, neutrons, pions, etc.? Do the loop corrections from QFT change the direction of spin magnetic moment from that of the net spin angular momentum in the fundamental and/or composite cases?
The eigenvalues (or measurable values) of each spin operator are ±1, corresponding to the only two mutually exclusive outcomes that could occur after a measurement of an electron's spin has been made. The mutual exclusivity is an experimental fact, but follows from the definition of the eigenstates above.In classical mechanics an electron has a magnetic moment, or spin vector, associated with it which, classically, can be measured continuously along each of its three spatial directions.In quantum mechanics, however, only one of the three components can be measured at a time, and there are only two possible values that can be measured.