  We investigate the ground state of the system of N bosons enclosed in a
hard-wall trap interacting via a repulsive or attractive $\delta$-function
potential. Based on the Bethe ansatz method, the explicit ground state wave
function is derived and the corresponding Bethe ansatz equations are solved
numerically for the full physical regime from the Tonks limit to the strongly
attractive limit. It is shown that the solution takes different form in
different regime. We also evaluate the one body density matrix and second-order
correlation function of the ground state for finite systems. In the Tonks limit
the density profiles display the Fermi-like behavior, while in the strongly
attractive limit the Bosons form a bound state of N atoms corresponding to the
N-string solution. The density profiles show the continuous crossover behavior
in the entire regime. Further the correlation function indicates that the Bose
atoms bunch closer as the interaction constant decreases.
