Order parameter at the boundary of a trapped Bose gas

Through a suitable expansion of the Gross-Pitaevskii equation near the classical turning point, we obtain an explicit solution for the order parameter at the boundary of a trapped Bose gas interacting with repulsive forces. The kinetic energy of the system, in terms of the classical radius R and of the harmonic oscillator length a(HO), follows the law E(kin)/N proportional to R(-2)[ln(R/a(HO)) + const], approaching, for large R, the results obtained by solving numerically the Gross-Pitaevskii equation. The occurrence of a Josephson-type current in the presence of a double trap potential is finally discussed.