Nonlinear Klein-Gordon equation and the Bose-Einstein condensation
Abstract
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 Schr\"odinger equation for the same systems as the relativistic effects diminish.
Cite
@article{arxiv.2110.14939,
title = {Nonlinear Klein-Gordon equation and the Bose-Einstein condensation},
author = {E. Megias and M. J. Teixeira and V. S. Timóteo and A. Deppman},
journal= {arXiv preprint arXiv:2110.14939},
year = {2022}
}
Comments
8 pages, 3 figures; v2 typos corrected, added references, extended discussion. It matches the version published in The European Physical Journal Plus