Abstract
We study the Klein–Gordon (KG) oscillator with a Cornell-type scalar confinement in (2+1)-dimensional Gürses space-time backgrounds and report their exact solutions. The effect of the vorticity parameter Omega on the energy levels is found to yield some interesting features like; energy levels-crossings, partial clustering of positive and negative energy levels, and shifting the energy gap upwards or downwards. Such confined KG-oscillators are also studied in a general deformed Gürses space-time background. Moreover, we consider the confined-deformed KG-oscillator from a (2+1)-dimensional Gürses to Gürses and pseudo-Gürses space-time backgrounds. The resulting confined-deformed KG-oscillators are found to admit invariance and isospectrality with each other.
Highlights
Inspired by the Dirac oscillator [1], the Klein–Gordon (KG) oscillator [2,3] has been a subject of intensive research in the last few decades
It has been shown that negative the gradient of the potential force field is no longer the time derivative of the canonical momentum p = m (x) x, but it is rather related to the time derivative of the pseu√do-momentum π (x) = m (x)x [30]
We started with a confined KG-oscillator in a Gürses space-time background (i.e. Gürses space-time metric ds2 (1) at specific parametric settings) and reported the corresponding exact solution in (17) and (23)
Summary
Inspired by the Dirac oscillator [1], the Klein–Gordon (KG) oscillator [2,3] has been a subject of intensive research in the last few decades. Khlevniuk [34] has argued that a point mass in the curved space may effectively be transformed into a PDM in Euclidean space Such coordinate transformation/deformation affects, in turn, the form of the canonical momentum in classical and the momentum operator in quantum mechanics (e.g., [29,30,33,37] and related references therein). The PDM momentum operator is constructed [33] and used to find the PDM creation and annihilation operators for the Schrödinger oscillator [29] It would be interesting, to investigate the effects of such PDM recipe [29,30,33,37] on the KG-oscillator in the (2+1)dimensional Gürses space-time backgrounds with a confinement. In the current methodical proposal, we consider the KG-oscillator confined in a Cornelltype scalar potential (i.e., S (r ) of (14) below, which is commonly used in quarkonium spectroscopy [19,43]) in a (2+1)-dimensional Gürses space-time backgrounds.
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