Comment on “Comment on Linear confinement of a scalar particle in a Gödel-type space-time”

Neto, Francisco A. Cruz; Soares, Camila C.; Castro, Luis B.

doi:10.1140/epjc/s10052-019-7603-9

Cited by 6 publications

(7 citation statements)

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“…Hereby, we have emphasized that the mathematical collapse of the KG-equation into the two dimensional radially symmetric Schrödinger-oscillator (hence the metaphoric notion of KG-oscillator emerged in the process) does not mean that the parametric characterizations are copied from one to the other. The parameter ω of (8) is not related to the angular frequencies of the harmonic oscillator (e.g., [46][47][48]50]) but rather admits values given by ω = ± |ΩE| (e.g., [45]). The usage of ω as the angular frequency of the harmonic oscillator had the consequences of losing at least half of the spectra (only positive energies were reported and anti-particle solutions were dismissed from the relativistic theory).…”

Section: Discussionmentioning

confidence: 99%

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PDM Klein-Gordon particles in Gödel-type Som-Raychaudhuri cosmic string spacetime background

Mustafa¹

2022

Preprint

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In Gödel-type Som-Raychaudhuri (SR) cosmic string spacetime background, we recycle the Klein-Gordon (KG) oscillators and report their correct exact solutions. We argue that the mathematical collapse of the KG-equation into the 2-dimensional radial Schrödinger-like oscillator does not yield that the parametric characterizations of one is inherited by the other. The angular frequency (positive) in the Schrödinger case is replaced by an irrational frequency-like (positive and negative) in the KG-case. Inheriting the Schrödinger oscillator's parametric characterizations implies that at least half of the spectra (the negative part) is lost in the process. We also introduce KGoscillators in pseudo-Gödel SR-type spacetime that admit invariance and isospectrality with those in Gödel SR-type spacetime background. We introduce position-dependent mass (PDM) settings to KG-particles in 4-vector and scalar Lorentz potentials in magnetic field in the Gödel SR-type spacetime background. Four illustrative examples of fundamental nature are discussed and their exact or conditionally exact solvability are reported. Amongst are, a PDM KG-Coulombic particle in 4-vector and scalar Coulombic Lorentz potentials in magnetic field, a PDM KG-Coulombic particle in 4-vector and scalar Coulombic Lorentz potentials in magnetic field at zero vorticity, a PDM KG-Coulombic particle in equally mixed 4-vector and scalar Coulombic Lorentz potentials in magnetic field, and a quasi-free PDM KG-oscillator. We also emphasis that the biconfluent Heun polynomial approach, to the effective oscillator plus Cornell type potential, yields conditionally exact solvability that paralyzes the solution from collapsing into that of pure Coulombic one.

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Section: Discussionmentioning

confidence: 99%

“…So should be the case with the results reported on the linear confinement of a scalar particle in Gödel-type space-time by Vitória [46] (their Eq. ( 23)) and in the related comment by Neto [47] (their Eq. ( 18)) for zero linear confinement.…”

Section: Introductionmentioning

confidence: 95%

PDM Klein-Gordon particles in Gödel-type Som-Raychaudhuri cosmic string spacetime background

Mustafa¹

2022

Preprint

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“…This would immediately result, in terms of the associated Laguerre polynomials ( ) as the exact eigen energies and eigen functions for the two dimensional Schr ödinger harmonic oscillator. Moreover, the same condition equation (35) should also be imposed on the biconfluent Heun function equation (33) so that a biconfluent Heun polynomial [43] of degree n = 2n r 0 is obtained (c.f., e.g., [23,41,44,45]) to imply…”

Section: Kg-particles In a 4-vector And Scalar Lorentz Potentials In ...mentioning

confidence: 99%

“…At this point, the truncation order n of a power series (biconfluent Heun function here) does not make it a valid quantum number, but rather it should be correlated to the well known quantum numbers as done above (i.e., n = 2n r 0). Hereby, one should give credentials for Neto and co-workers [23] as they resemble a group of the very few who have correctly used condition equation (35) on the biconfluent Heun polynomials. Only under such condition that the result of equation (38) would recover those of equation ( 36) for a = 0 = b.…”

Section: Kg-particles In a 4-vector And Scalar Lorentz Potentials In ...mentioning

confidence: 99%

“…Moreover, the covariant and contravariant metric tensors associated with the Som-Raychaudhuri spacetime are, respectively, given by The objective of the current methodical proposal is to explore in a comprehensive manner the effect of the gravitational field generated by the Gödel-type cosmic string SR-spacetime equation (2) on the spectra of some Klein-Gordon (KG) particles of fundamental quantum gravity nature, like the KG-oscillators and KG-Coulomb models. Such fundamental models have been studied by different authors (e.g., [12][13][14][15][16][17][18][22][23][24]) where the vorticity parameter Ω is assumed to take the form Ω 0 and the energies are assumed to be positive…”

Section: Introductionmentioning

confidence: 99%

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Klein–Gordon particles in Gödel-type Som-Raychaudhuri cosmic string spacetime and the phenomenon of spacetime associated degeneracies

Mustafa¹

2022

Phys. Scr.

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We argue that only exact, comprehensive, and explicit solutions for the fundamental models (i.e., the Klein-Gordon (KG) oscillators and the KG-Coulomb) would help to understand and describe the effects of gravitational fields on the dynamics of such quantum mechanical systems. In the current methodical proposal, the effects of the gravitational fields generated by a Gödel-type Som-Raychaudhuri (SR) cosmic string spacetime on KG-oscillators (KG-particles in general) are studied and reported. In so doing, we revisit the KG-oscillators in a topologically trivial Gödel-type spacetime background and use textbook procedures to report its exact solution that covers even and odd parities. Next, we discuss the drawbacks associated with the power series expansion approach that implies the biconfluent Heun functions/polynomials solution. We, therefore, recollect the so called pseudo perturbative shifted ` expansion technique (PSLET) as an alternative and more sophisticated method/technique. Illustrative examples are used: (i) a KG-oscillator in a topologically trivial Gödel-type spacetime, (ii) a quasi-free KG-oscillator in Gödel SR-type cosmic string spacetime, (iii) a KG-Coulombic particle in Gödel SR-type cosmic string spacetime at zero vorticity, and (iv) a massless KG-particle in Gödel SR-type cosmic string spacetime in a Cornell-type Lorentz scalar potential. The corresponding exact energies are obtained from the zeroth (leading) order correction of PSLET, where all higher order correction identically vanish. The comprehensive exactness of the reported solutions manifestly suggest degeneracies associated with spacetime (STAD) phenomenon.

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

Mustafa

2022

Annals of Physics

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Comment on “Comment on Linear confinement of a scalar particle in a Gödel-type space-time”

Cited by 6 publications

References 6 publications

PDM Klein-Gordon particles in Gödel-type Som-Raychaudhuri cosmic string spacetime background

PDM Klein-Gordon particles in Gödel-type Som-Raychaudhuri cosmic string spacetime background

Klein–Gordon particles in Gödel-type Som-Raychaudhuri cosmic string spacetime and the phenomenon of spacetime associated degeneracies

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

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