Configuration weight function method to solve the many-body Schr\"{o}dinger equation

TL;DR

This paper introduces a novel configuration weight function method for solving the many-body Schrödinger equation, which improves accuracy and convergence over traditional methods by using interaction potential surfaces and configuration-dependent coefficients.

Contribution

The method employs configuration weight functions dependent on interaction potential surfaces, offering a variational approach that surpasses conventional configuration interaction in accuracy and convergence.

Findings

Method provides upper bounds for ground state energy.

More accurate than traditional CI with fewer configurations.

Achieves near-CI accuracy with fewer basis functions.

Abstract

A method to solve the Schr\"{o}dinger equation based on the use of constant particle-particle interaction potential surfaces is proposed. The many-body wave function is presented in configuration interaction form with coefficients - configuration weight functions - dependent on the total interaction potential. A set of linear ordinary differential equations for the configuration weight functions was developed and solved for particles in a infinite well and He-like ions. The results demonstrate that the method is variational and provides upper bound for energy of the ground state; even in its lowest two-body interaction potential surfaces approximation, it is more accurate than the conventional configuration interaction method and demonstrates a better convergence with a basis set increase. For He-like ions one configuration approximation with non-interaction electrons functions are used as basis set the calculated energies are below the Hartree-Fock limit. In three configuration approximations the accuracy of energy calculation is close to CI accuracy with 35 configuration taking into account. Four configurations give the energies below CI method and slightly below precise calculation with Hylleraas type wave functions.