On a relativistic particle and a relativistic position-dependent mass particle subject to the Klein–Gordon oscillator and the Coulomb potential

Abstract

The relativistic quantum dynamics of an electrically charged particle subject to the Klein-Gordon oscillator and the Coulomb potential is investigated. By searching for relativistic bound states, a particular quantum effect can be observed: a dependence of the angular frequency of the KleinGordon oscillator on the quantum numbers of the system. The meaning of this behaviour of the angular frequency is that only some specific values of the angular frequency of the Klein-Gordon oscillator are permitted in order to obtain bound state solutions. As an example, we obtain both the angular frequency and the energy level associated with the ground state of the relativistic system. Further, we analyse the behaviour of an electrically charged particle subject to the Klein-Gordon oscillator, the Coulomb potential and a linear scalar potential.

Linear confinement of a scalar particle in a Gödel-type spacetime

“…Note that the problem which is investigated in this work is very different from that investigated in Refs. [37][38][39]. Here, we investigate the relativistic spinless quantum particle in a rotating spacetime in the presence of a topological defect.…”

“…We recover the results of Refs. [37][38][39] in the appropriate limits. In this way, the results (18) correspond to the bound state associated with the radial mode n = 1, where the allowed energies depend on the rotation parameter and the parameter α, which characterizes the cosmic string.…”

“…It is worth to point out that the linear scalar potential has attracted a great interest in atomic and molecular physics [23][24][25][26][27][28][29] and in relativistic quantum mechanics [30][31][32][33][34][35][36][37][38][39]. Our objective is to investigate the effects of the background defined in Eq.…”

Relativistic quantum motion of spin-0 particles under the influence of noninertial effects in the cosmic string spacetime

“…In recent years, several studies have addressed the Klein-Gordon oscillator in quantum systems [49][50][51][52][53][54][55][56][57]. It has a formulation similar to the vector potential in the previous section, so to study its solutions we will use the following change in momentum operator:…”

Klein–Gordon oscillator in Kaluza–Klein theory

“…In a recent paper, Boumali and Messai [35] have investigated a Klein-Gordon oscillator in the background of cosmic strings in the presence of a uniform magnetic field. The Klein-Gordon oscillator was investigated in the presence of a Coulomb potential considering two ways of coupling of Coulomb potential within the Klein-Gordon equation: in the first paper [36] the Coulomb potential is incorporated in the equation by a modification mass term, in the second model [37] this potential is introduced in the Klein-Gordon equation via the minimal coupling, in the latter case the linear potential also was included in the equation. Our intention now is to extend these studies not only to other dimensions but mostly to consider this dynamics in general background spacetimes produced by topological defects using KaluzaKlein theory [2,[38][39][40][41][42].…”