DOI: https://doi.org/10.26089/NumMet.v25r435

On the possibility of using the NNQS for the Klein–Gordon–Fock equation

Authors

  • Aleksandr M. Kalitenko
  • Petr I. Pronin

Keywords:

quantum mechanics
neural network
Klein–Gordon–Fock equation

Abstract

In this article, we present a method for finding quantum stationary states of the Klein–Gordon–Fock (KGF) equation using neural networks (NNs). The method has been tested on two well-known systems: a relativistic spinless particle in a Coulomb potential, and a one-dimensional relativistic harmonic oscillator. The results of training the neural network for these two systems are presented, as well as the analysis of the training process. The neural network method shows a good agreement with analytical calculations (if they can be found explicitly), providing a promising approach for solving more complex problems in quantum physics and quantum chemistry.

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Published

2024-12-09

Issue

Vol. 25 (2024): Issue 4.

Section

Methods and algorithms of computational mathematics and their applications

Author Biographies

Aleksandr M. Kalitenko

Lomonosov Moscow State University,
Faculty of Physics,
Leninskie Gory, 1, building 2, 119991, Moscow
• Ph.D. student

Petr I. Pronin

Lomonosov Moscow State University,
Faculty of Physics,
Leninskie Gory, 1, building 2, 119991, Moscow
• Associate Professor

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