A deep neural network approach to solve the Dirac equation
Quantum Physics
2025-07-17 v2 Other Condensed Matter
Nuclear Theory
Atomic Physics
Computational Physics
Abstract
We extend the method from [Naito, Naito, and Hashimoto, Phys. Rev. Research 5, 033189 (2023)] to solve the Dirac equation not only for the ground state but also for low-lying excited states using a deep neural network and the unsupervised machine learning technique. The variational method fails because of the Dirac sea, which is avoided by introducing the inverse Hamiltonian method. For low-lying excited states, two methods are proposed, which have different performances and advantages. The validity of this method is verified by the calculations with the Coulomb and Woods-Saxon potentials.
Cite
@article{arxiv.2412.03090,
title = {A deep neural network approach to solve the Dirac equation},
author = {Chuanxin Wang and Tomoya Naito and Jian Li and Haozhao Liang},
journal= {arXiv preprint arXiv:2412.03090},
year = {2025}
}
Comments
16 pages, 16 figures, 3 tables