Klein Gordon Oscillator Research Articles

Comment on “Confined Klein–Gordon oscillators in Minkowski spacetime and a pseudo-Minkowski spacetime with a space-like dislocation: PDM KG-oscillators, isospectrality and invariance”

We argue that the analytical energies obtained recently in Mustafa (2022) from a radial eigenvalue equation are incorrect because the truncation method used by the author forces a relationship between two model parameters. This relationship (overlooked by the author) depends on the truncation number and as a result the exact analytical energies do not correspond to a single model but are solutions to different physical models. The reason is that the radial eigenvalue equation is not exactly solvable but conditionally solvable so that one can only obtain some particular exact solutions. We also show that the exact eigenvalues obtained for a particular simpler case are also incorrect because the author overlooked that the shift of the radial coordinate leads to a change in the left boundary condition.

Effects of Lorentz symmetry breaking environment on generalized relativistic quantum oscillator field

In this paper, we study the generalized Klein–Gordon oscillator under the effects of the violation of Lorentz symmetry defined by a tensor field ( KF) μναβ out of the standard model extension. We consider a possible scenario of Lorentz-violating with a Cornell-type potential form electric field and a linear magnetic field that contributes a harmonic-type central potential effects in the quantum motions of oscillator fields. The bound-state solutions of the wave equation using the parametric Nikiforov–Uvarov method by considering Coulomb- and Cornell-type potential form functions are obtained. We see that the eigenvalue solutions get modified by the Lorentz symmetry breaking effects in comparison to the Landau levels (without Lorentz-violation effects in flat space).

Comment on “PDM Klein–Gordon oscillators in cosmic string spacetime in magnetic and Aharonov–Bohm flux fields within the Kaluza–Klein theory”

We show that the spectra of some models with supposed physical utility derived recently are not correct. The eigenvalues to the radial differential equations do not satisfy well-known theorems. The origin of the problem is that those equations are not exactly solvable but conditionally solvable. Present analysis shows that the author overlooked a second condition that provides a relationship between the model parameters. Consequently, all the conclusions derived from those supposedly exact eigenvalues cannot be correct.

Confined Klein–Gordon oscillators in Minkowski spacetime and a pseudo-Minkowski spacetime with a space-like dislocation: PDM KG-oscillators, isospectrality and invariance

We revisit a confined (in a Cornell-type Lorentz scalar potential) KG-oscillator in Minkowski spacetime with space-like dislocation background. We show that the effect of space-like dislocation is to shift the energy levels along the dislocation parameter axis, and consequently energy levels crossings are unavoidable. We report some KG-particles in a pseudo-Minkowski spacetime with space-like dislocation that admit isospectrality and invariance with the confined KG-oscillator in Minkowski spacetime with space-like dislocation. An alternative PDM setting for the KG-particles (relativistic particles in general) is introduced. We discuss the effects of space-like dislocation and PDM settings on the confined KG-oscillators in Minkowski spacetime with space-like dislocation. Three confined PDM KG-oscillators are discussed as illustrative examples, (i) a PDM KG-oscillator from a dimensionless scalar multiplier gr=exp(2αr2)≥0,α≥0, (ii) a PDM KG-oscillator from a power law type dimensionless scalar multiplier gr=Arσ≥0, and (iii) a PDM KG-oscillator in a Cornell-type confinement with a dimensionless scalar multiplier gr=expξr≥0 .

Dunkl–Klein–Gordon Equation in Three-Dimensions: The Klein–Gordon Oscillator and Coulomb Potential

Recent studies show that deformations in quantum mechanics are inevitable. In this contribution, we consider a relativistic quantum mechanical differential equation in the presence of Dunkl operator-based deformation and we investigate solutions for two important problems in three-dimensional spatial space. To this end, after introducing the Dunkl quantum mechanics, we examine the Dunkl-Klein-Gordon oscillator solutions with the Cartesian and spherical coordinates. In both coordinate systems, we find that the differential equations are separable and their eigenfunctions can be given in terms of the associate Laguerre and Jacobi polynomials. We observe how the Dunkl formalism is affecting the eigenvalues as well as the eigenfunctions. As a second problem, we examine the Dunkl-Klein-Gordon equation with the Coulomb potential. We obtain the eigenvalue, their corresponding eigenfunctions, and the Dunkl-fine structure terms.

Generalized quantum oscillator under harmonic-type central potential effects induced by Lorentz symmetry violation environment(a)

In this paper, we study a relativistic quantum oscillator model via the generalized Klein-Gordon oscillator equation under harmonic-type central potential effects induced by the violation of the Lorentz symmetry. We determine solutions of the wave equation for Coulomb- and Cornell-type potential functions using the Nikiforov-Uvarov method and analyze the effects on the energy profile and the wave function of the oscillator fields.

Exact solution of generalized KG-oscillator under Lorentz-violating effects by a fixed vector field subject to interaction potential

In this work, the relativistic quantum oscillator under the Lorentz symmetry violation environment defined by an arbitrary constant vector field [Formula: see text] is analyzed. We solve the generalized Klein–Gordon oscillator with different vector field configurations and obtained the bound-states solutions. After that, we insert a static Coulomb-type scalar potential in the wave equation and solve the generalized Klein–Gordon oscillator analytically. We discuss the effects of Lorentz symmetry violation and the Coulomb-type potential on the energy spectrum of these oscillator fields.

Effects of Lorentz symmetry breaking by a tensor field subject to Coulomb-type potential on relativistic quantum oscillator

In this paper, we solve the Klein–Gordon oscillator analytically under Lorentz-violating effects defined by a tensor field subject to a Coulomb-type scalar potential. We obtain the bound-state solutions of the quantum system by choosing various electromagnetic field configurations and discuss the effects on the energy profiles and the wave function of these oscillator fields.

Relativistic motions of spin-zero quantum oscillator field in a global monopole space-time with external potential and AB-effect

In this paper, we analyze a spin-zero relativistic quantum oscillator in the presence of the Aharonov–Bohm magnetic flux in a space-time background produced by a point-like global monopole (PGM). Afterwards, we introduce a static Coulomb-type scalar potential and subsequently with the same type of vector potential in the quantum system. We solve the generalized Klein–Gordon oscillator analytically for different functions (e.g. Coulomb- and Cornell-type functions) and obtain the bound-states solutions in each case. We discuss the effects of topological defects associated with the scalar curvature of the space-time and the Coulomb-type external potentials on the energy profiles and the wave function of these oscillator fields. Furthermore, we show that the obtained energy eigenvalues depend on the magnetic quantum flux which gives rise to the gravitational analogue of the Aharonov–Bohm (AB) effect.

Effects of Lorentz symmetry violation by a constant vector field subject to Cornell-type potential on relativistic quantum oscillator

In this paper, we analyze a relativistic quantum oscillator model under a Lorentz symmetry violation (LSV) environment defined by an arbitrary constant vector field [Formula: see text] subject to Cornell-type scalar potential. We first introduce the Cornell-type scalar potential by modifying the mass term via [Formula: see text], and then momentum vector [Formula: see text] in the wave equation. We solve the Klein–Gordon oscillator analytically for different vector field configurations and obtained the bound-states energy profiles and the wave function. We discuss the influences of a vector field on the energy eigenvalues and the wave function of these oscillators.

Relativistic quantum oscillator model under the effects of the violation of Lorentz symmetry by an arbitrary fixed vector field

We study a spin-zero relativistic quantum oscillator model under the violation of Lorentz symmetry defined by an arbitrary constant vector field . We solve the Klein-Gordon oscillator using the Nikiforov-Uvarov method and obtain the bound-states solutions of the quantum system. We see that vector field configurations modify the energy profile of the oscillator fields.

PDM Klein–Gordon oscillators in cosmic string spacetime in magnetic and Aharonov–Bohm flux fields within the Kaluza–Klein theory

In the cosmic string spacetime and within Kaluza–Klein theory (KKT) backgrounds (indulging magnetic and Aharonov-Bohm flux fields), we introduce and study position-dependent mass (PDM) Klein–Gordon (KG) oscillators. The effective PDM is introduced as a deformation/defect in the momentum operator. We show that there are four different ways to obtain KG-oscillator. Two of which are readily known and the other two are obtained as byproducts of PDM settings. Next, we provide a thorough analysis on the corresponding spectra under different parametric effects, including the curvature parameter’s effect. Such analysis is used as a reference/lead model which is used in the discussion of different PDM KG-oscillators models: a mixed power-law and exponential type PDM model that yields a pseudo-confined PDM KG-oscillator in cosmic string spacetime within KKT (i.e., the PDM KG-oscillators are confined in their own PDM manifested Cornell-type confinement), and a PDM KG-oscillator confined in a Cornell-type potential. Moreover, we extend our study and discuss a non-Hermitian PT-symmetric PDM-Coulombic-type KG-particle model in cosmic string spacetime within KKT.

Non-commutativity and non-inertial effects on a scalar field in a cosmic string space-time: I. Klein–Gordon oscillator

We analyse the Klein–Gordon oscillator in a cosmic string space-time and study the effects stemming from the rotating frame and non-commutativity in momentum space. We show that the latter mimics a constant magnetic field, imparting physical interpretation to the setup. The field equation for the scalar field is solved via separations of variables, and we obtain quantization of energy and angular momentum. The space-time metric is non-degenerate as long as the particle is confined within a hard-wall, whose position depends on the rotation frame velocity and the string mass parameter. We investigate the energy quantization both for a finite hard-wall (numerical evaluation) and in the limit of an infinite hard-wall (analytical treatment). We stress the effect of non-commutativity upon the energy quantization in each case.

Klein–Gordon oscillator under the effects of violation of Lorentz symmetry

In this paper, the behavior of a Klein–Gordon oscillator under Lorentz symmetry breaking determined by a tensor [Formula: see text] out of the Standard Model Extension (SME) is analyzed. We choose a scenario of Lorentz-violating with an electric field inversely proportional to the radial and/or axial distance, and a constant magnetic field along [Formula: see text]-direction. In this analysis, we see that the Lorentz-violating terms modified the energy spectrum and the wave function of an oscillator field in comparison to the known standard Landau levels. Furthermore, we note that the oscillation frequency [Formula: see text] of a scalar particle depends on quantum numbers [Formula: see text] as well as on Lorentz-violating parameters in the quantum system which shows a quantum effect.

Generalized Klein-Gordon oscillator in Lorentz symmetry violation framework

In this paper, the generalized Klein-Gordon oscillator is studied in the framework of Lorentz symmetry violation, and the Nikiforov-Uvarov method is used to analyze the Klein-Gordon oscillator with and without magnetic field. On this basis, we analyze some special cases of Klein-Gordon oscillators with Cornell potential functions in detail. The results show that the wave function and the energy eigenvalues of the generalized Klein-Gordon oscillator obviously depend on the Lorentz symmetry violation effect, and the Cornell potential function also has a non-negligible effect on the Klein-Gordon oscillator.

Gravitational effects of a cloud of strings on the generalized Klein–Gordon oscillator in the presence of Coulomb-type potential

Gravitational effects of a cloud of strings on the generalized Klein–Gordon oscillator in the presence of Coulomb-type potential

Confined Klein-Gordon Oscillators in a Spacetime and a Pseudo-Spacetime with a Space-Like Dislocation: Pdm Kg-Oscillators, Isospectrality and Invariance

Confined Klein-Gordon Oscillators in a Spacetime and a Pseudo-Spacetime with a Space-Like Dislocation: Pdm Kg-Oscillators, Isospectrality and Invariance

Klein–Gordon oscillator in a global monopole space–time with rainbow gravity

Klein–Gordon oscillator in a global monopole space–time with rainbow gravity

Central potential effects induced by Lorentz symmetry violation on modified quantum oscillator field

In this paper, effects of Lorentz symmetry violation determined by a tensor field [Formula: see text] out of the Standard Model Extension on a modified quantum oscillator field in the presence of Cornell-type scalar potential are analyzed. We first introduced a scalar potential [Formula: see text] by modifying the mass square term via transformation [Formula: see text] in the Klein–Gordon equation, and then replace the momentum operator [Formula: see text], where [Formula: see text] is an arbitrary function other than [Formula: see text] to study the modified Klein–Gordon oscillator. We solve the wave equation and obtain the analytical bound-states solutions and see the dependence of oscillator frequency [Formula: see text] on the quantum numbers [Formula: see text] as well as on Lorentz-violating parameters with the potential which shows a quantum effect.

Klein-Gordon oscillator under a linear central potential induced by Lorentz symmetry violation

The Klein-Gordon oscillator under Lorentz symmetry violation determined by the tensor out of the Standard Model Extension (SME) is analyzed. We introduce angular frequency of the oscillator with a Klein-Gordon particle by replacing the momentum vector in the wave equation. We choose the scenario of Lorentz symmetry violation with the field configuration of a constant magnetic field along the z-direction and a cylindrical electric field along the radial direction. We then solved the wave equation and obtained the bound state solutions of the modified Klein-Gordon oscillator. We see that the angular frequency of oscillator depends on the quantum numbers of the system which shows a quantum effect and on Lorentz symmetry breaking parameters.