  The low-energy-level macroscopic wave functions of the Bose-Einstein
condensate(BEC) trapped in a symmetric double-well and a periodic potential are
obtained by solving the Gross-Pitaevskii equation numerically. The ground state
tunnel splitting is evaluated in terms of the even and odd wave functions
corresponding to the global ground and excited states respectively. We show
that the numerical result is in good agreement with the analytic level
splitting obtained by means of the periodic instanton method.
