  Bi-local mean field theory is applied to one dimensional quantum liquid with
long range $1/r^2$ interaction, which has exact ground state wave function. We
obtain a mean field solution and an effective action which expresses a long
range dynamics. Based on them the ground state energy and correlation functions
are computed. The ground state energy agrees fairly well with the exact value
and exponents have weaker coupling constant dependence than that of partly
known exact value.
