First principles physics-informed neural network for quantum wavefunctions and eigenvalue surfaces
This work provides a parametric and analytical solution for quantum systems, useful for applications like force field determination, but it is incremental as it builds on existing physics-informed neural network methods.
The authors tackled the problem of discovering parametric eigenvalue and eigenfunction surfaces for quantum systems by proposing a physics-informed neural network, achieving realistic wavefunctions with cusps for the hydrogen molecular ion as a continuous and differentiable function of interatomic distance.
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.