Quantum mechanical particles like electrons, protons, or atoms have an instrinsic angular momentum or spin. For electrons and protons the spin in a particular direction, e.g. z-direction, can take on one of two values +/- hbar/2. The operators associated with the spin observable are S_z = (hbar/2) sigma_z, S_x = (hbar/2) sigma_x, and S_y = (hbar/2) sigma_y. These particles also have an intrinsic magnetic moment, M = gamma S, where S is the spin and gamma is the gyromagnetic ratio. This intrinsic magnetic moment was seen in the Stern-Gerlach experiment. Because the spin operators, S_x, S_y, S_z, do not commute, two components of the spin can not be measured simultaneously.