  This study builds upon the work of Palacios and MacDonald (Phys. Rev. Lett.
{\bf 76}, 118 (1996)), wherein they identify the bosonic excitations of Wen's
approach for the edge of the 1/3 fractional quantum Hall state with certain
operators introduced by Stone. Using a quantum Monte Carlo method, we extend to
larger systems containing up to 40 electrons and obtain more accurate
thermodynamic limits for various matrix elements for a short range interaction.
The results are in agreement with those of Palacios and MacDonald for small
systems, but offer further insight into the detailed approach to the
thermodynamic limit. For the short range interaction, the results are
consistent with the chiral Luttinger liquid predictions.We also study
excitations using the Coulomb ground state for up to nine electrons to
ascertain the effect of interactions on the results; in this case our tests of
the chiral Luttinger liquid approach are inconclusive.
