Nonlinear Klein–Gordon equation and the Bose–Einstein condensation
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
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
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