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arXiv · 1908.02785

Algebraic structures and deformed Schr\"{o}dinger equations from groups entropies

Ignacio S. Gomez·Ernesto P. Borges
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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 $q$-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.

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BibTeXRIS

Ignacio S. Gomez, Ernesto P. Borges. 2019-08-07. Algebraic structures and deformed Schr\"{o}dinger equations from groups entropies. https://arxiv.org/abs/1908.02785

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