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arXiv · 2110.14939

Nonlinear Klein-Gordon equation and the Bose-Einstein condensation

E. Megias·M. J. Teixeira·V. S. Timóteo·A. Deppman
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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.

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E. Megias, M. J. Teixeira, V. S. Timóteo, A. Deppman. 2021-10-28. Nonlinear Klein-Gordon equation and the Bose-Einstein condensation. https://doi.org/10.1140/epjp%2Fs13360-022-02511-2

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