New method of solving the many-body Schr\"odinger equation

TL;DR

This paper introduces a novel approach to solving the many-body Schrödinger equation using interaction potential surfaces, improving accuracy and convergence over traditional methods.

Contribution

The paper proposes a new method utilizing constant particle-particle interaction potential surfaces, with a hierarchy of approximations that enhances computational efficiency and accuracy.

Findings

More accurate than conventional configuration interaction methods

Demonstrates better convergence with basis set increase

Validated on simple solvable models and He-like ions

Abstract

A method of solving the Schr\"{o}dinger equation based on the use of constant particle-particle interaction potential surfaces (IPS) is proposed. The many-body wave function is presented in a configuration interaction form, with coefficients depending on the total interaction potential. The corresponding set of linear ordinary differential equations for the coefficients was developed. To reduce the computational work, a hierarchy of approximations based on interaction potential surfaces of a part of the particle system was worked out. The solution of a simple exactly solvable model and He-like ions proves that this method is more accurate than the conventional configuration interaction method and demonstrates a better convergence with a basis set increase.