Numerical tests of the envelope theory for few-boson systems

TL;DR

This paper evaluates the envelope theory's effectiveness in approximating the ground states of few-boson systems and proposes a modification to enhance its accuracy.

Contribution

It introduces a modification to the envelope theory to improve approximation accuracy for few-boson Hamiltonian problems.

Findings

The envelope theory provides reasonable ground state estimates.

Modifying the quantum number improves approximation quality.

The method is applicable across various bosonic systems.

Abstract

The envelope theory, also known as the auxiliary field method, is a simple technique to compute approximate solutions of Hamiltonians for $N$ identical particles in $D$-dimension. The accuracy of this method is tested by computing the ground state of $N$ identical bosons for various systems. A method is proposed to improve the quality of the approximations by modifying the characteristic global quantum number of the method.