Solving the Schrödinger equation with machine learning

Abstract

The Schrödinger equation is known to be a great tool for understanding small physical systems, yet an analytical solution exists solely for some simple cases. As a consequence of this, a wide variety of numerical methods are used to solve real systems, and machine learning methods, namely Artificial Neural Networks (ANNs), are amidst the newest. In this work we use an ANN to find the ground state wave function of the deuteron -this is, the nuclear two-body bound state-, achieving energy values that are within 0.05% of the exact results and wave functions that overlap up to 99.9997% with the exact ones. We also compare the performance of a single-layer ANN against a two-layer ANN, the latter not showing significant improvements over the former