The generalized Klein–Gordon oscillator in the background of cosmic string space-time with a linear potential in the Kaluza–Klein theory
Eur. Phys. J. C
(2020) 80:211
https://doi.org/10.1140/epjc/s10052-020-7781-5
Regular Article - Theoretical Physics
The generalized Klein–Gordon oscillator in the background
of cosmic string space-time with a linear potential in the
Kaluza–Klein theory
Faizuddin Ahmeda
Ajmal College of Arts and Science, Dhubri 783324, Assam, India
Received: 4 November 2019 / Accepted: 26 February 2020
© The Author(s) 2020
Abstract In this work, we study the generalized Klein–
Gordon oscillator with interactions on a curved background
within the Kaluza–Klein theory. We solve the generalized
Klein–Gordon oscillator in the cosmic string space-time with
a linear scalar potential and obtain the energy eigenvalue
and corresponding eigenfunction. We show that the energy
spectrum depends on the global parameters characterizing
the space-time and the confining potential parameter. We also
solve the generalized Klein–Gordon oscillator in a magnetic
cosmic string background in the Kaluza–Klein theory with a
linear scalar potential and analyze the analogue effect to the
Aharonov–Bohm effect for bound states.
1 Introduction
The relativistic quantum dynamics of scalar and spin- 21 particles on curved background space-time geometries as well
as Gödel, and Gödel-type metrics have been investigated by
various authors (see [1] and references therein). The Klein–
Gordon and Dirac equations in a Gödel-type space-times with
positive, zero and negative curvatures were first studied in
[2]. The close relationship between the quantum dynamics
of the scalar particle in the background of general relativity
with the Gödel solutions and the Landau levels in flat, spherical and hyperbolic spaces were investigated in [3,4]. Later,
the same problem was studied by solving the Klein–Gordon
equation in the Som–Raychaudhuri space-time in [5]. The
authors in [6] solved the Klein–Gordon equation in a family
of Gödel-type solutions with the cosmic string and analyzed
the similarity of the energy eigenvalue with the Landau levels
in flat, spherical and hyperbolic spaces. Quantum influence
of topological defects in a Gödel-type space-times in flat,
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spherical and hyperbolic cases, were investigated in [7]. The
relativistic quantum dynamics of a Dirac particle with topological defects in a Gödel-type space-times with torsion have
been investigated in [8]. The relativistic quantum dynamics
of an electrically charged particle described by the Klein–
Gordon oscillator subject to a Coulomb-type potential was
investigated in [9]. Weyl fermions in a family of Gödel-type
geometries with topological defects were investigated in [10].
The relativistic quantum dynamics of a scalar particle in 4D
curved space-time with the cosmic string was investigated in
[11]. The relativistic quantum dynamics of scalar and spin1
2 particles subject to various kind of potentials have been
investigated in several areas of physics (e.g., [12–26]). Linear confinement of quantum particle by introducing a linear
scalar potential into the relativistic system by modifying the
mass term has great importance for models of confinement
of quarks [27]. It is worth mentioning that the linear scalar
potential has attracted a great interest in atomic and molecular
physics [28–33], and in the relativistic quantum mechanics
[9,34–50].
Interactions of the Dirac oscillator with the gravitational
fields produced by topological defects were investigated in
[51]. The influence of Aharonov–Casher effect on the Dirac
oscillator in three different scenarios of general relativity:
the Minkowski space-time, the cosmic string and the cosmic
dislocation space-time were studied in [52]. The influence
of non-inertial effects on the Dirac oscillator in the cosmic
string space-time was investigated in [53]. The Dirac equation in a class of topologically trivial flat Gödel-type spacetime was investigated in [54]. Dirac fermions in the Som–
Raychaudhuri space-time with a linear scalar and vector
potentials were investigated in [36]. A new model for study
the confinement of spin-half particles in a two-dimensional
quantum ring systems described by the Dirac equation with
a new coupling were studied in [55]. The Dirac oscillator in
the context of Doubly General Relativity was investigated in
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[56]. Effects of gravitational fields produced by topological
defects on the Dirac field and oscillator in a spinning cosmic string was examined in [57]. The dynamics of 2D Dirac
oscillator in the space-time of a magnetic cosmic string were
investigated in [58]. The generalized Dirac oscillator in the
cosmic string space-time replacing the momentum pμ with
its alternative pμ + m ω β f μ (xμ ) was studied in [59]. In particular, the quantum dynamics was considered for the function f μ (xμ ) to be taken as Cornell-type, exponential-type
and singular potentials form. The generalized Dirac oscillator was introduced in (2 + 1)-dimensional the world [60]. The
Dirac oscillator under the influence of non-inertial effects in
a rotating frame in the cosmic string space-time were investigated in [61]. The Dirac oscillator has also been analyzed
in various physical systems, such as in the presence of external fields [62], and in the presence of a magnetic quantum
flux [63–66]. Investigation of magnetization and persistent
current of mass-less Dirac fermions confined in a quantum
dot in a graphene layer with topological defects were done in
[67]. Non-inertial effects on the Dirac oscillator in the background space-time generated by a cosmic string have been
investigated [68–70]. The (1 + 2)-dimensional Dirac oscillator in the presence of a homogeneous magnetic field in an
Aharonov–Casher system were investigated in [71]. The relativistic quantum dynamics of spin-half particle by solving
the Dirac equation in (1 + 2)-dimensional Gürses space-time
was investigated in [72].
The Klein–Gordon oscillator [73,74] was inspired by
the Dirac oscillator [75] applied to half-integer spin particles. The spectral distribution of energy levels and eigenfunction describing the state of a particle by solving the
Klein–Gordon equation in one-dimensional version of the
Minkowski space-time were studied in [76]. The Klein–
Gordon oscillator in the cosmic string space-time in the
presence of external fields were studied in [77]. The Klein–
Gordon oscillator in the presence of a Coulomb-type potential was investigated by two ways: (1) by modifying the mass
term m → m + S(r ) [78] and (2) via the minimal coupling
[9] besides a linear scalar potential. The relativistic quantum effects on the Klein–Gordon oscillator with linear scalar
and Coulomb-type potentials were investigated in [49]. The
Klein–Gordon oscillator has also been investigated in various physical system, such as in the background space-time
generated by the cosmic string [79], in the background of a
Gödel-type space-time under the influence of gravitational
fields produced by topolog (...truncated)
