  We carry out a detailed examination of the ground state property of few-boson
system in a one-dimensional hard wall potential with a $\delta -$ split in the
center. In the Tonks-Girardeau limit with infinite repulsion between particles,
we use the Bose-Fermi mapping to construct the exact $N-$ particle ground state
wavefunction which allows us to study the correlation properties accurately.
For the general case with finite inter-particle interaction, the exact
diagonalization method is exploited to study the ground-state density
distribution, occupation number distribution, and momentum distribution for
variable interaction strengths and barrier heights. The secondary peaks in the
momentum distribution reveal the interference between particles on the two
sides of the split, which is more prominent for large barrier strength and
small interaction strength.
