The generalized Klein–Gordon oscillator in the background of cosmic string space-time with a linear potential in the Kaluza–Klein theory

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.

Effects of Kaluza-Klein Theory and Potential on a Generalized Klein-Gordon Oscillator in the Cosmic String Space-Time

“…In Ref. [34], the relativistic quantum dynamics of a scalar particle subject to linear potential on the curved background within the Kaluza-Klein theory was studied. We have solved the generalized Klein-Gordon oscillator in the cosmic string and magnetic cosmic string space-time with a linear potential within the Kaluza-Klein theory.…”

“…Aharonov-Bohm effect [19][20][21] is a quantum mechanical phenomena that has been investigated in several branches of physics, such as in, graphene [22], Newtonian theory [23], bound states of massive fermions [24], scattering of dislocated wave-fronts [25], torsion effect on a relativistic position-dependent mass system [26,27], and nonminimal Lorentz-violating coupling [28]. In addition, Aharonov-Bohm effect has been investigated in the context of Kaluza-Klein theory by several authors [18,[29][30][31][32][33][34], and the geometric quantum phase in graphene [35]. It is well-known in condensed matter [36][37][38][39][40] and in the relativistic quantum systems [41,42] that when there exists dependence of the energy eigenvalues on geometric quantum phase [21], then, persistent current arises in the systems.…”

“…We consider a generalization of the oscillator as described in Refs. [34,64] for the Klein-Gordon. This generalization is introduced through a generalized momentum operator where the radial coordinate r is replaced by a general function f ðrÞ.…”

“…To generalized the Klein-Gordon oscillator, we adopted the idea considered in Refs. [34,64,66,68,69] by replacing r ⟶ f ðrÞ as…”

“…We choose the function f ðrÞ a Cornell-type given by [34,64,66,69] Substituting the function (11) and Cornell potential (6) into the Eq. (9), we obtain the following equation:…”