Solving the two dimensional Schr\"odinger equation using basis truncation: a controversial case

TL;DR

This paper investigates the use of basis truncation to solve the two-dimensional Schrödinger equation for two interacting electrons, revealing that the method's validity depends on the interaction type.

Contribution

It highlights the controversial and unexplained dependence of the matrix approach's correctness on the interaction type in a two-electron system.

Findings

Matrix approach validity varies with interaction type

Basis truncation can lead to inconsistent solutions

Highlights need for careful method selection in quantum systems

Abstract

Solutions of the Schr\"odinger equation by spanning the wave function is a complete basis is a common practice is many-body interacting systems. We shall study the case of a two-dimensional quantum system composed by two interacting spin-less electrons and see that the correctness of the matrix approach depends inexplicably on the type of interaction existing between particles.