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<p>The Neural Network Quantum State (NNQS) approach offers a novel way to solve problems in quantum physics. Although this technique has been successful in addressing various issues, further research is needed to understand its full potential and limitations. In this study, we propose a neural network-based solution for the spinless particle within the Schwarzschild metric for three coordinate systems and compare it with the solution of the Klein–Gordon–Fock equations with a Coulomb potential. Our approach bridges the gap between analytic and numerical methods, improving the quality and usefulness of future studies in this field.</p>

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Neural Network Quantum States in Curved Spacetime

  • 期刊论文

  • 发表日期：

    2026年2月7日

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  • A. M. Kalitenko,
  • P. I. Pronin

摘要

The Neural Network Quantum State (NNQS) approach offers a novel way to solve problems in quantum physics. Although this technique has been successful in addressing various issues, further research is needed to understand its full potential and limitations. In this study, we propose a neural network-based solution for the spinless particle within the Schwarzschild metric for three coordinate systems and compare it with the solution of the Klein–Gordon–Fock equations with a Coulomb potential. Our approach bridges the gap between analytic and numerical methods, improving the quality and usefulness of future studies in this field.