Confined Klein–Gordon oscillator from a (2+1)-dimensional Gürses to a Gürses or a pseudo-Gürses space-time backgrounds: Invariance and isospectrality

Mustafa, Omar

doi:10.1140/epjc/s10052-022-10043-3

Cited by 17 publications

(6 citation statements)

References 51 publications

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“…Present expression for W is not consistent with Mustafa's results ( 5) and (10) unless n = 2n r . However, this discrepancy is irrelevant because neither E M , γM…”

Section: Physical Modelscontrasting

confidence: 98%

“…Those equations are conditionally solvable and one obtains some particular polynomial solutions for particular values of the model parameters determined by a second condition overlooked by Mustafa. This conclusion also applies to another paper by the same author where he apparently derived exact results for a similar conditionally-solvable problem [10]. Most physical conclusions commonly derived from the polynomial solutions to conditionally-solvable eigenvalue equations are meaningless [2][3][4].…”

Section: Discussionmentioning

confidence: 52%

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On the misinterpretation of conditionally-solvable quantum-mechanical problems

Fernández¹

2022

Preprint

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We apply the Frobenius (power-series) method to some simple exactlysolvable and conditionally-solvable quantum-mechanical models with supposed physical interest. We show that the supposedly exact solutions to radial eigenvalue equations derived in recent papers are not correct because they do not satisfy some well-known theorems. We also discuss the origin of the mistake by means of the approach indicated above.

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“…Present expression for W is not consistent with Mustafa's results ( 5) and (10) unless n = 2n r . However, this discrepancy is irrelevant because neither E M , γM…”

Section: Physical Modelscontrasting

confidence: 98%

Section: Discussionmentioning

confidence: 52%

On the misinterpretation of conditionally-solvable quantum-mechanical problems

Fernández¹

2022

Preprint

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“…(see e.g. [27,28,35], and the same recipe can be used for KG-Coulombic particles as well). This would, in turn, yield…”

Section: Kg-particles In a Qpgm Spacetime Backgroundmentioning

confidence: 99%

“…For both illustrative examples above, one should notice that the two KG-oscillators in (33) and (35) in the QPGM spacetime of (5) are invariant and isospectral with the KG-oscillators in (28) in the PGM spacetime of (3).…”

Section: Power-law Type Metric Function Q(ρ) = Bρ υmentioning

confidence: 99%

Klein–Gordon particles in a quasi-pointlike global monopole spacetime and a Wu-Yang magnetic monopole: invariance and isospectrality

Mustafa

2024

J. Phys. G: Nucl. Part. Phys.

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We use two correlated metric functions and transform/deform the pointlike global monopole (PGM) spacetime metric into a quasi-PGM (QPGM) spacetime one. We study Klein-Gordon (KG) particles(manifestly introduced by the non-minimal coupling form of the operator $%\tilde{D}_{\mu }=D_{\mu }+\mathcal{F}_{\mu }$, with $\mathcal{F}_{\mu }$ $%\in %TCIMACRO{\U{211d} }%%BeginExpansion\mathbb{R}%EndExpansion$, and $D_{\mu }=\partial _{\mu }-ieA_{\mu }$) in such QPGM spacetime background. We show that the KG-particles in the QPGM spacetime are isospectral and invariant with KG-particles in the PGM spacetime, provided that the two metric functions are correlated. The Wu-Yang magnetic monopole (WYMM) is also included in the process. We report the effects of both monopoles PGM/QPGM and WYMM on the spectroscopic structure of two models, KG-oscillators and KG-Coulomb particles in such spacetime background. Moreover, we discuss KG-Coulomb particles and shifted KG-oscillators in a PGM spacetime and a WYMM, where such models are manifestly introduced by some Lorentz scalar interaction potentials $S(r)$. The current study is not only of fundamental observability nature but also of pedagogical interest in quantum gravity.

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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%

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 oscillator from a (2+1)-dimensional Gürses to a Gürses or a pseudo-Gürses space-time backgrounds: Invariance and isospectrality

Cited by 17 publications

References 51 publications

On the misinterpretation of conditionally-solvable quantum-mechanical problems

On the misinterpretation of conditionally-solvable quantum-mechanical problems

Klein–Gordon particles in a quasi-pointlike global monopole spacetime and a Wu-Yang magnetic monopole: invariance and isospectrality

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

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