Perturbative treatment of the non-linear q-Schrödinger and q-Klein-Gordon equations

M. C. ROCCA; D.J. ZAMORA; G.L. FERRI; A. PLASTINO

ENTROPY

MOLECULAR DIVERSITY PRESERVATION INTERNATIONAL-MDPI

Lugar: Basel; Año: 2017 vol. 19 p. 1 - 11

1099-4300

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.