Effects of a linear central potential induced by the Lorentz symmetry violation on the Klein–Gordon oscillator

Abstract

Inspired by the Standard Model Extension, we have investigated a possible scenario arising from the Lorentz symmetry violation governed by a background tensor field on a scalar field subject to the Klein-Gordon oscillator, where this possible scenario gives rise to a linear central potential. We analyse the behaviour of the relativistic quantum oscillator under the influence of a Coulomb-type scalar potential in this background. Then, we solve the Klein-Gordon equation analytically and discuss the influence of the background which violates the Lorentz symmetry in the relativistic energy levels.

Klein-Gordon Oscillator Under the Effects of the Cornell-Type Interaction in the Kaluza-Klein Theory

“…Energy relativistic effects appearing in these quantum systems with position-dependent mass have been investigated. Interesting properties emerge in systems with quarkantiquark interaction [28], with pionic atom [29], in the spacetime with curvature [30][31][32], in the spacetime with torsion [33][34][35][36], in the Som-Raychaudhuri spacetime [37][38][39], in possible scenarios of Lorentz symmetry violation [40][41][42], on the Klein-Gordon oscillator (KGO) [43][44][45][46], in solution of the Dirac equation in a conical spacetime [47] and in Kaluza-Klein theory (KKT) [48][49][50]. The procedure of inserting central potentials into relativistic wave equations is given by the transformation m → m + S( r) [29], where m is the rest mass and S( r) is the scalar potential.…”

Klein-Gordon Oscillator in the Presence of External Fields in a Cosmic Space-Time with a Space-Like Dislocation and Aharonov-Bohm Effect

“…Here, we investigate the above relativistic quantum system described by the Klein-Gordon oscillator subject to a Cornell-type scalar potential in the presence of external fields including an internal magnetic flux field. A scalar potential is included into the systems by modifying the mass m ⟶ m + SðrÞ which is called a position-dependent mass system in the relativistic quantum systems (see, e.g., [5,6,8,28,30,31,42,46,[52][53][54][55][56][57][58][59][60][61][62]).…”

“…Recently, the Cornell potential has been studied in the ground state of three quarks [63]. However, this type of potential is worked on spherical symmetry; in cylindrical symmetry, which is in our case, this type of potential is known as a Cornell-type potential [8,31,[54][55][56].…”

Quantum Influence of Topological Defects on a Relativistic Scalar Particle with Cornell-Type Potential in Cosmic String Space-Time with a Spacelike Dislocation

“…Several authors have studied the relativistic wave-equations with various kind of potentials such as linear, Coulomb-type, Cornell-type etc. (e. g., [3,5,7,19,51,52,53,56,57,59,60]). Using the equation 3, Eq.…”