Test of a Jastrow-type wavefunction for a trapped few-body system in one dimension

TL;DR

This paper tests a simple Jastrow-type wavefunction for a few-body quantum system in one dimension, showing it accurately estimates ground state energies with minimal error, based on a trial wavefunction inspired by two-particle solutions.

Contribution

The study introduces and numerically validates a Jastrow-type wavefunction ansatz for one-dimensional trapped few-body systems, demonstrating its effectiveness in energy estimation.

Findings

Ground state energy estimates within ~1% error

Wavefunction accurately captures two-particle correlations

Method effective for very small systems

Abstract

For a system with interacting quantum mechanical particles in a one-dimensional harmonic oscillator, a trial wavefunction with simple structure based on the solution of the corresponding two-particle system is suggested and tested numerically. With the inclusion of a scaling parameter for the distance between particles, at least for the very small systems tested here the ansatz gives a very good estimate of the ground state energy, with the error being of the order of ~1% of the gap to the first excited state.