Abstract
In this contribution we study the Klein-Gordon oscillator on the curved background within the Kaluza-Klein theory. The problem of interaction between particles coupled harmonically with a topological defects in Kaluza-Klein theory is studied. We consider a series of topological defects, that treat the Klein-Gordon oscillator coupled to this background and find the energy levels and corresponding eigenfunctions in these cases. We show that the energy levels depend on the global parameters characterizing these spacetimes. We also investigate a quantum particle described by the Klein-Gordon oscillator interacting with a cosmic dislocation in Som-Raychaudhuri spacetime in the presence of homogeneous magnetic field in a Kaluza-Klein theory. In this case, the spectrum of energy is determined, and we observe that these energy levels are the sum of the term related with Aharonov-Bohm flux and of the parameter associated to the rotation of the spacetime.
Highlights
Several studies have demonstrated an interest in relativistic models [19,20,21,22] where the interaction potential is similar to the one of the harmonic oscillator, such as the vibrational spectrum of diatomic molecules [23], the binding of heavy quarks [24,25], and the oscillations of atoms in crystal lattices, by mapping them as a position-dependent mass system [26,27,28,29]
The Klein–Gordon oscillator in the Som– Raychaudhuri spacetime in the presence of uniform magnetic fields was investigated by Wang et al [52]. This contribution is organized as follows: in Sect. 2, using the Kaluza–Klein theory, we study the energy levels of particles interacting with a gravitational field produced by a cosmic string in the presence of a Klein–Gordon oscillator
The eigenvalues (42) represent the energy levels for a free scalar particle in a Som–Raychaudhuri spacetime pierced by a cosmic dispiration and a uniform magnetic field introduced in a geometric way by Kaluza–Klein theory
Summary
Several studies have demonstrated an interest in relativistic models [19,20,21,22] where the interaction potential is similar to the one of the harmonic oscillator, such as the vibrational spectrum of diatomic molecules [23], the binding of heavy quarks [24,25], and the oscillations of atoms in crystal lattices, by mapping them as a position-dependent mass system [26,27,28,29]. Our intention now is to extend these studies to other dimensions but mostly to consider this dynamics in general background spacetimes produced by topological defects using Kaluza– Klein theory [2,38,39,40,41,42] These sources of gravitational fields play an important role in condensed matter physics systems [43,44,45,46], mainly due to the possibility to compensate for the elastic contribution introduced by the defect by fine tuning of the external magnetic field.
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