Ground State of a One-Dimensional Many-Boson System

The ground state of a one-dimensional system of many bosons interacting through a repulsive $\delta$-function potential is studied when the coupling parameter $\gamma$ of the system is small. The procedure is based on the variational analysis in the Bijl-Dingle-Jastrow wave-function space. The ground-state energy, determined in a series form in powers of ${\gamma }^{\frac{1}{2}}$ and truncated after the third leading term, is found to be in fair agreement with exact results of Lieb and Liniger over a range of the coupling parameter extending up to $\gamma =6\mathrm{}$. Two slightly different approaches are considered, and they are shown to be equivalent.