Algebraic structures and deformed Schr\"{o}dinger equations from groups entropies
Abstract
Motivated by the group entropy theory, in this work we generalize the algebra of real numbers (that we called G-algebra), from which we develop an associated G-differential calculus. Thus, the algebraic structures corresponding to the Tsallis and Kappa statistics are obtained as special cases when the Tsallis and Kappa group classes are chosen. We employ the G-algebra to formulate a generalized G-deformed Schr\"{o}dinger equation and we illustrate it with the infinite potential well, where the effective mass is related with the G-algebra structure and the -deformed (standard) Schr\"{o}dinger equation results an special case for the Tsallis (Boltzmann-Gibbs) group class. The non-uniform zeros spacing of the G-deformed eigenfunctions is expressed in terms of the generalized sum of the G-algebra.
Cite
@article{arxiv.1908.02785,
title = {Algebraic structures and deformed Schr\"{o}dinger equations from groups entropies},
author = {Ignacio S. Gomez and Ernesto P. Borges},
journal= {arXiv preprint arXiv:1908.02785},
year = {2019}
}