Schr\"odinger equation solved for the hydrogen molecule with unprecedented accuracy

TL;DR

This paper presents a highly precise solution to the nonrelativistic Schrödinger equation for the hydrogen molecule, achieving unprecedented accuracy to enhance physical constant determination and tests of fundamental forces.

Contribution

It provides the first nonrelativistic Schrödinger equation solution for H₂ with accuracy of 10^{-12}, surpassing previous theoretical predictions.

Findings

Achieved 10^{-12} accuracy in solving the Schrödinger equation for H₂

Improves theoretical predictions for molecular hydrogen levels

Facilitates better tests of fundamental physics

Abstract

The hydrogen molecule can be used for determination of physical constants and for improved tests of the hypothetical long range force between hadrons, which requires a sufficiently accurate knowledge of the molecular levels. For this reason, we have undertaken a project of significant improvements in theoretical predictions of H$_2$ and perform the first step, which is the solution of the nonrelativistic Schr\"odinger equation to the unprecedented accuracy of $10^{-12}$. This will inspire, we hope, a parallel progress in the spectroscopy of the molecular hydrogen.