On the Dirac oscillator subject to a Coulomb-type central potential induced by the Lorentz symmetry violation
Departamento de Física e Química, Universidade Federal do Espírito Santo, Av. Fernando Ferrari, 514, Goiabeiras, Vitória, ES, 29060-900, Brazil
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Accepted: 31 January 2020
Published online: 13 February 2020
We investigated the relativistic oscillator model for spin-1/2 fermionic fields, known as the Dirac oscillator, in a background of breaking the Lorentz symmetry governed by a constant vector field inserted in the Dirac equation by non-minimal coupling, where we proposed two possible scenarios of Lorentz symmetry violation which induce a Coulomb-type potential. Thus, in the search for solutions of bound states, we determine, analytically, the relativistic energy profile for the Dirac oscillator, where an interesting quantum effect arises: The frequency of the Dirac oscillator is determined by the quantum numbers of the system and the parameters that characterize the scenarios of Lorentz symmetry violation.
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