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

Abstract

We have investigated the interaction between the Klein-Gordon oscillator and the Cornell-type potential in a background characterized by the Kaluza-Klein theory, where it is governed by the manifestation of the extra dimension through the Aharonov-Bohm effect for bound states. Then, in the search for bound state solutions, we analytically determine the relativistic energy profile of the oscillator under the effects of Cornell-type interaction and for the particular cases of Coulomb-type and linear potentials, where in all cases, the frequency of the relativistic oscillator has restricted values determined by the quantum numbers of the system.

Linear confinement of generalized KG-oscillator with a uniform magnetic field in Kaluza–Klein theory and Aharonov–Bohm effect

“…In this way, we can work with general relativity in five-dimensions. The information about the electromagnetism is given by introducing a gauge potential in the space-time 26 , 29 , 30 as where , is the time-coordinate, is the coordinate associated with fifth additional dimension having ranges where, a is the radius of the compact dimension of y , are the cylindrical coordinates with the usual ranges, and is the gauge coupling or Kaluza constant 29 . The parameter 61 characterizing the wedge parameter where, is the linear mass density of the string.…”

“…The relativistic quantum dynamics of spin-0 scalar particle with a scalar potential S ( r ) by modifying the mass term in the form as done in Refs. 27 , 28 , 48 in five-dimensional case is described by 26 , 31 – 33 : where , with is the determinant of metric tensor with its inverse for the line element ( 2 ) and m is rest mass of the particle.…”

“… 25 , KG-oscillator field interacts with Cornell-type potential in Ref. 26 , generalized KG-oscillator in the background of magnetic cosmic string with scalar potential of Cornell-type in Ref. 27 , generalized KG-oscillator in the background of magnetic cosmic string with a linear confining potential in Ref.…”

“… 46 – 48 ). In the context of KKT, the KG-oscillator in five-dimensional cosmic string and magnetic cosmic string background 25 , under a Cornell-type potential in five-dimensional Minkowski space-time 26 have investigated. In addition, generalized KGO on curved background space-time induced by a spinning cosmic string coupled to a magnetic field including quantum flux 49 , in magnetic cosmic string background under the effects of Cornell-type potential 27 and a linear confining potential 28 using KKT, in the presence of Coulomb-type potential in -dimensions Gürses space–time 50 , in cosmic string space-time with a spacelike dislocation 51 , and in cosmic string space-time 52 have investigated.…”

Quantum Effects on KG-Oscillator Feld Under a Cornell-Type Potential in Kaluza-Klein Theory

“…In Ref. [47], interaction between KG-oscillator and scalar potential of different kinds in the five-dimensional Minkowski space-time background using Kaluza-Klein theory was investigated. In this paper, we study the same problem in the background of the five-dimensional cosmic string space-time with a uniform magnetic field using Kaluza-Klein theory.…”