This article is cited in 2 papers

Methods and algorithms of computational mathematics and their applications

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

A. M. Kalitenko, P. I. Pronin

Lomonosov Moscow State University, Faculty of Physics

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.

Keywords: quantum mechanics, neural network, Klein–Gordon–Fock equation.

Received: 17.09.2024

Language: English

DOI: 10.26089/NumMet.v25r435