Up to now, we have considered quantum particles to have three degrees
of freedom,
,
, and
. This, then, leads to three quantum
numbers that characterize the states. For example, in a central
potential, the three quantum numbers are
,
and
, the
radial, total angular momentum, and
-component of angular momentum
numbers, respectively.
However, there is substantial experimental evidence to suggest that there are additional degrees of freedom still missing from this simple picture that need to be accounted for. Some of this evidence will be reviewed below.