Volume 129, Number 1, January 2020
|Number of page(s)||7|
|Published online||12 February 2020|
Non-additive quantum mechanics for a position-dependent mass system: Dirac delta and quasi-periodic potentials
1 Instituto Federal de Educação, Ciência e Tecnologia do Sertão Pernambucano Rua Maria Luiza de Araújo Gomes Cabral s/n, 56316-686 Petrolina, Pernambuco, Brazil
2 Instituto de Física, Universidade Federal da Bahia - Campus Universitário de Ondina 40170-115 Salvador, Bahia, Brazil
3 Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems Rua Xavier Sigaud 150, Rio de Janeiro, RJ 22290-180, Brazil
Received: 30 September 2019
Accepted: 23 January 2020
Motivated by non-extensive statistical mechanics, in this work we consider a deformed Schrödinger equation (DSE) for position-dependent mass (PDM) systems, whose deformed plane-wave solutions allow to characterise a non-periodic lattice. We obtain a deformed version of the Bloch theorem and we illustrate the formalism presented with two examples of the literature: the Dirac and the Kronig-Penney potentials. We found that the Kronig-Penney potential offers a modelling for a lattice with defects expressed by a non-periodicity of the potential within the underlying non-extensive mathematical structure, which is evidenced by the displacement of the gaps with respect to the non-deformed case. The eigenfunctions, the reduced energy bands scheme and the density of states are affected by the deformation.
PACS: 03.65.Ca – Formalism / 71.20.-b – Electron density of states and band structure of crystalline solids / 05.90.+m – Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems (restricted to new topics in section 05)
© EPLA, 2020
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