We establish a new geometric wave function that combined with a variational principle efficiently describes a system of bosons interacting in a one-dimensional trap. By means of a a combination of the exact wave function solution for contact interact
ions and the asymptotic behaviour of the harmonic potential solution we obtain the ground state energy, probability density and profiles of a few boson system in a harmonic trap. We are able to access all regimes, ranging from the strongly attractive to the strongly repulsive one with an original and simple formulation.
