Consider the Chern-Simons topological quantum field theory with gauge group
SU(2) and level k. Given a knot in the 3-sphere, this theory associates to the
knot exterior an element in a vector space. We call this vector the knot state
and study its asymptotic properties when the level is large. The latter vector
space being isomorphic to the geometric quantization of the SU(2)-character
variety of the peripheral torus, the knot state may be viewed as a section
defined over this character variety.