Consider an isolated system whose center of mass is at rest. Let the eigenvalue of the system's total angular momentum be . According to the theory of orbital angular momentum outlined in the previous chapter, there are two possibilities. For a system consisting of a single particle, . For a system consisting of two (or more) particles, is a non-negative integer. However, these predictions do not agree with experimental observations, because we often encounter single-particle systems that have . Even worse, multi-particle systems in which has half-integer values abound in nature. In order to explain this apparent discrepancy between theory and experiments, Goudsmit and Uhlenbeck (in 1925) introduced the concept of an internal, purely quantum mechanical, angular momentum called spin . For a single-particle system with spin, the total angular momentum in the rest frame is non-vanishing.