  We determine the action of the Kauffman bracket skein algebra of the torus on
the Kauffman bracket skein module of the complement of the 3-twist knot. The
point is to study the relationship between knot complements and their boundary
tori, an idea that has proved very fruitful in knot theory. We place this idea
in the context of Chern-Simons theory, where such actions arose in connection
with the computation of the noncommutative version of the A-polynomial that was
defined by Frohman, Gelca and Lofaro, but they can also be interpreted as
quantum mechanical systems. Our goal is to exhibit a detailed example in a part
of Chern-Simons theory where examples are scarce.
