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* [58]. For a single-particle system with spin, the total angular momentum in the
rest frame is non-vanishing.