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

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.