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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'sapproach for the edge of the 1/3 fractional quantum Hall state with certainoperators introduced by Stone. Using a quantum Monte Carlo method, we extend tolarger systems containing up to 40 electrons and obtain more accuratethermodynamic limits for various matrix elements for a short range interaction.The results are in agreement with those of Palacios and MacDonald for smallsystems, but offer further insight into the detailed approach to thethermodynamic limit. For the short range interaction, the results areconsistent with the chiral Luttinger liquid predictions.We also studyexcitations using the Coulomb ground state for up to nine electrons toascertain the effect of interactions on the results; in this case our tests ofthe chiral Luttinger liquid approach are inconclusive.

Electron operator at the edge of the 1/3 fractional quantum Hall liquid