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

• URL: http://arxiv.org/abs/2211.04607v1
• Date: Tue, 8 Nov 2022 23:22:42 GMT
• Title: First principles physics-informed neural network for quantum wavefunctions and eigenvalue surfaces
• Authors: Marios Mattheakis, Gabriel R. Schleder, Daniel Larson, Efthimios Kaxiras
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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