  With the aim of the extension of the TDHF theory in the canonical form in the
Lipkin model, the trial state for the variation is constructed, which is an
extension of the Slater determinant. The canonicity condition is imposed to
formulate the variational approach in the canonical form. A possible solution
of the canonicity condition is given and the zero-point fluctuation induced by
the uncertainty principle is investigated. As an application, the ground state
energy is evaluated.
