  The Tonks-Girardeau model is a quantum mechanical model of N impenetrable
bosons in 1+1 dimensions. A Vandermonde determinant provides the exact
N-particle wave function of the ground state, or equivalently the matrix
elements with respect to position eigenstates. We consider the large $N$ limit
of these matrix elements. We present a binning prescription which calculates
the leading terms of the matrix elements in a time which is independent of $N$,
and so is suitable for this limit. In this sense, it allows one to solve for
the ground state of a strongly coupled continuum quantum field theory in the
field eigenstate basis. As examples, we calculate the matrix elements with
respect to states with uniform density and also states consisting of two
regions with distinct densities.
