Confined Klein-Gordon oscillators in Minkowski spacetime and a pseudo-Minkowski spacetime with a space-like dislocation: PDM KG-oscillators, isospectrality and invariance

Abstract

We revisit the a confined (in a Cornell-type Lorentz scalar potential) KG-oscillator in Minkowski spacetime with space-like dislocation background. We show that the effect of space-like dislocation is to shift the energy levels along the dislocation parameter axis, and consequently energy levels crossings are unavoidable. We report some KG-particles in a pseudo-Minkowski spacetime with space-like dislocation that admit isospectrality and invariance with the confined KG-oscillator in Minkowski spacetime with space-like dislocation. An alternative PDM setting for the KG-particles (relativistic particles in general) is introduced. We discuss the effects of space-like dislocation and PDM settings on the confined KG-oscillators in Minkowski spacetime with space-like dislocation. Three confined PDM KG-oscillators are discussed as illustrative examples, (i) a PDM KG-oscillator from a dimensionless scalar multiplier $g\left(r\right)=exp(2\alpha r^2)\ge 0,\alpha \ge 0$, (ii) a PDM KG-oscillator from a power law type dimensionless scalar multiplier $g\left(r\right)=A{r}^{\sigma }\ge 0$, and (iii) a PDM KG-oscillator in a Cornnell-type confinement with a dimensionless scalar multiplier $g\left(r\right)=\exp \left(\xi r\right)\ge 0$

17 pages, 3 Figures

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• PDM relativistic quantum oscillator in Einstein-Maxwell-Lambda space-time
• Klein-Gordon particles in a quasi-pointlike global monopole spacetime and a Wu-Yang magnetic monopole: invariance and isospectrality
• Schrödinger oscillators in a deformed point-like global monopole spacetime and a Wu-Yang magnetic monopole: position-dependent mass correspondence and isospectrality
• PDM Klein-Gordon particles in Som-Raychaudhuri cosmic string spacetime with space-like dislocation and a non-uniform magnetic field: spacetime associated degeneracies, vorticity-energy, and charge-energy correlations
• Klein-Gordon particles in Gödel-type Som-Raychaudhuri cosmic string spacetime and the phenomenon of spacetime associated degeneracies
• KG-oscillators in Eddington-inspired Born-Infeld gravity: Wu-Yang magnetic monopole and Ricci scalar curvature effects
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