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 Schrödinger equation for the same systems as the relativistic effects diminish.

Comments: 8 pages, 3 figures; v2 typos corrected, added references, extended discussion. It matches the version published in The European Physical Journal Plus