First principles physics-informed neural network for quantum wavefunctions and eigenvalue surfaces

TL;DR

This paper introduces a physics-informed neural network that learns continuous, differentiable quantum wavefunctions and eigenvalues for molecular systems, enabling efficient parametric solutions to the Schrödinger equation.

Contribution

It presents a novel neural network approach to discover parametric eigenvalue and eigenfunction surfaces for quantum systems, including realistic wavefunctions with physical features.

Findings

Successfully solves the Schrödinger equation for hydrogen molecular ion

Produces continuous, differentiable wavefunctions with physical cusps

Enables analytical derivatives for further physical calculations

Abstract

Physics-informed neural networks have been widely applied to learn general parametric solutions of differential equations. Here, we propose a neural network to discover parametric eigenvalue and eigenfunction surfaces of quantum systems. We apply our method to solve the hydrogen molecular ion. This is an ab-initio deep learning method that solves the Schrodinger equation with the Coulomb potential yielding realistic wavefunctions that include a cusp at the ion positions. The neural solutions are continuous and differentiable functions of the interatomic distance and their derivatives are analytically calculated by applying automatic differentiation. Such a parametric and analytical form of the solutions is useful for further calculations such as the determination of force fields.