Improvement of the envelope theory with the dominantly orbital state method

TL;DR

This paper enhances the envelope theory for N-body quantum systems by integrating the dominantly orbital state method, improving the accuracy of approximate eigenvalues through a new parameter optimization approach.

Contribution

It introduces a novel method to optimize the envelope theory using the dominantly orbital state, leading to more precise eigenvalue approximations for many-body Hamiltonians.

Findings

Improved eigenvalue accuracy demonstrated on several systems.

The method effectively determines the optimal global quantum number parameter.

Enhanced envelope theory applicability to N-body quantum problems.

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 $D$ dimensions. The quality of the approximate eigenvalues can be improved by adding a free parameter in the characteristic global quantum number of the solutions. A method is proposed to determine the value of this parameter by comparing the eigenvalues computed with the envelope theory to the corresponding ones computed with a $N$-body generalization of the dominantly orbital state method. The accuracy of the procedure is tested with several systems.