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Algebraic structures and position-dependent mass Schrödinger equation from group entropy theory

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Abstract

Based on the group entropy theory, in this work, we generalize the algebra of real numbers (referred to as G-algebra) along with its associated calculus, thus obtaining the algebraic structures corresponding to the Tsallis and the \(\kappa \)-statistics. From a G-deformed translation operator, we obtain its associated Schrödinger equation, that corresponds to a particle with an effective position-dependent mass determined by the G-algebra. The q-deformed (standard) Schrödinger equation results in a special case for the Tsallis (Boltzmann–Gibbs) group class. We illustrate the results with the one-dimensional potential well for the \(\kappa \) and the Tsallis classes and we obtain a family of potentials associated with the group entropy classes by first principles.

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Funding

ISG and EPB acknowledge support received from the National Institute of Science and Technology for Complex Systems (INCT-SC) and from the National Council for Scientific and Technological Development (CNPq) (at Universidade Federal da Bahia), Brazil.

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  1. Instituto de Física, Universidade Federal da Bahia, Rua Barao de Jeremoabo, Salvador, Bahia, 40170-115, Brasil

    Ignacio S. Gomez & Ernesto P. Borges

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  1. Ignacio S. Gomez
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  2. Ernesto P. Borges
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Correspondence to Ignacio S. Gomez.

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Gomez, I.S., Borges, E.P. Algebraic structures and position-dependent mass Schrödinger equation from group entropy theory. Lett Math Phys 111, 43 (2021). https://doi.org/10.1007/s11005-021-01387-0

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