First principles physics-informed neural network for quantum wavefunctions and eigenvalue surfaces
arXiv preprint arXiv:2211.04607, 2022•arxiv.org
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 …
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 …
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.
arxiv.org