https://doi.org/10.1140/epjp/s13360-022-02511-2
Regular Article
Nonlinear Klein–Gordon equation and the Bose–Einstein condensation
1
Departamento de Física Atómica, Molecular y Nuclear and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071, Granada, Spain
2
Instituto de Física, Universidade de São Paulo, 05508-090, São Paulo, P, Brazil
3
Grupo de Óptica e Modelagem Numérica, Faculdade de Tecnologia GOMNI/FT, Universidade Estadual de Campinas - UNICAMP, 13484-332, Limeira, SP, Brazil
Received:
16
November
2021
Accepted:
22
February
2022
Published online:
9
March
2022
The interest in the Klein–Gordon equation with different potentials has increased in recent years due to its possible applications in Cosmology, Hadron Physics and High-Energy Physics. In this work, we investigate the solutions of the Klein–Gordon equation for bosons under the influence of an external potential by using the Feshbach–Villars method. We present detailed results for two cases: the Coulombic potential and the harmonic potential. For the latter case, we studied the effects of self-interacting particles by adopting a mean-field approach. We show that our results converge smoothly to the solution of the Schrödinger equation for the same systems as the relativistic effects diminish.
© The Author(s) 2022
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
