A geometric wave function for few interacting bosons in a harmonic trap

TL;DR

This paper introduces a new geometric wave function combined with a variational principle to efficiently describe few interacting bosons in a one-dimensional harmonic trap across all interaction regimes.

Contribution

It presents a novel wave function formulation that unifies exact solutions and asymptotic behaviors for bosons in a harmonic trap, covering all interaction strengths.

Findings

Accurate ground state energy calculations across interaction regimes

Probability density and profiles matching known limits

Unified approach for attractive and repulsive interactions

Abstract

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 interactions 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.