info:eu-repo/semantics/article
Perturbative treatment of the non-linear q-schrödinger and q-Klein-Gordon equations
Fecha
2017-01Registro en:
Zamora, Darío Javier; Rocca, Mario Carlos; Plastino, Ángel Luis; Ferri, Gustavo Luis; Perturbative treatment of the non-linear q-schrödinger and q-Klein-Gordon equations; Molecular Diversity Preservation International; Entropy; 19; 1; 1-2017; 1-11
1099-4300
CONICET Digital
CONICET
Autor
Zamora, Darío Javier
Rocca, Mario Carlos
Plastino, Ángel Luis
Ferri, Gustavo Luis
Resumen
Interesting non-linear generalization of both Schrödinger's and Klein-Gordon's equations have been recently advanced by Tsallis, Rego-Monteiro and Tsallis (NRT) in Nobre et al. (Phys. Rev. Lett. 2011, 106, 140601). There is much current activity going on in this area. The non-linearity is governed by a real parameter q. Empiric hints suggest that the ensuing non-linear q-Schrödinger and q-Klein-Gordon equations are a natural manifestations of very high energy phenomena, as verified by LHC-experiments. This happens for q-values close to unity (Plastino et al. (Nucl. Phys. A 2016, 955, 16-26, Nucl. Phys. A 2016, 948, 19-27)). It might thus be difficult for q-values close to unity to ascertain whether one is dealing with solutions to the ordinary Schrödinger equation (whose free particle solutions are exponentials and for which q = 1) or with its NRT non-linear q -generalizations, whose free particle solutions are q-exponentials. In this work, we provide a careful analysis of the q ~ 1 instance via a perturbative analysis of the NRT equations.