Two-Dimensional Klein–Gordon Oscillator in the Presence of a Minimal Length

Boumali, Abdelmalek; Selama, Z.

doi:10.1134/s1547477118050047

Cited by 5 publications

(3 citation statements)

References 27 publications

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“…In addition, it is worth considering further cases with general noncommutative configuration variables (such as section 3) and other possibilities such as [X, Π X ] = if(Π X , Π Y ) (see [44,45] for example), by classical and quantum approaches.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

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Classical and quantum bicosmology with noncommutativity

Kan¹,

Aoyama²,

Shiraishi³

2022

Class. Quantum Grav.

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Recently, Falomir, Gamboa, Mendez, Gondolo and Maldonado proposed a bicosmology scenario [1-4] for solving some cosmological problems related to inflation, dark matter, and thermal history of the universe. Their plan is to introduce noncommutativity into the momentum space of the two scale factors. In the present paper, we revisit their model and first consider exact classical solutions in the model with constant noncommutativity between dynamical variables and between canonical momenta. We also hypothesize that the noncommutativity appears when the scale factors are small, and show the behavior of the classical solution in that case with momentum-space noncommutativity. Finally, we write down the Wheeler-DeWitt equation in that case and examine the behavior of the solution.

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Section: Conclusion and Discussionmentioning

confidence: 99%

“…For a constant β, the solution for ψ L (r) which is finite at r = 0 is expressed by using the confluent hypergeometric function as [44,45]:…”

Section: Noncommutativity In Momenta For Small Scale Factors: Quantum...mentioning

confidence: 99%

Classical and quantum bicosmology with noncommutativity

Kan¹,

Aoyama²,

Shiraishi³

2022

Class. Quantum Grav.

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“…For example, in the presence of the ML, Jana et al obtained an exact solutions to the KG equation by employing a linear and vector potential energy [24]. In 2018, Boumali et al investigated a two dimensional KG oscillator under the GUP [25]. In another study, Elviyanti et al employed Asymptotic Iteration Method to examine the Hultén potential energy in the KG equation in the ML [26].…”

Section: Introductionmentioning

confidence: 99%

Thermal properties of a two-dimensional Duffin-Kemmer-Petiau oscillator under an external magnetic field in the presence of a minimal length

Aounallah,

Lütfüoğlu,

Kříž

2019

Preprint

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In this article, we investigate the solutions of a two-dimensional Duffin-Kemmer-Petiau (DKP) oscillator within an external magnetic field in a minimal length (ML) formalism of the Heisenberg generalized uncertainty principle. First, we obtain the eigensolutions in the ordinary quantum mechanics. Then, we examine the DKP oscillator in the presence of a ML for the spin-zero and spin-one sectors. We determine an energy eigenvalue equation in both cases with the corresponding eigenfunctions. We show that in the limit where the ML correction vanishes, the energy eigenvalue equations become identical with the habitual quantum mechanical ones. Finally, we employ the Euler-Mclaurin summation formula and obtain the thermodynamic functions of the DKP oscillator in the high-temperature scale. We conclude that in the literature there are several articles with the misleading thermal properties of the relativistic oscillators.

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Klein-Gordon Oscillator In Dynamical Noncommutative Space

Haouam

2024

Int J Theor Phys

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Two-Dimensional Klein–Gordon Oscillator in the Presence of a Minimal Length

Abstract: Minimal length of a two-dimensional Klein-Gordon oscillator is investigated and illustrates the wave functions in the momentum space. The energy eigenvalues are found and the corresponding wave functions are calculated in terms of hyper-geometric functions.

Cited by 5 publications

References 27 publications

Classical and quantum bicosmology with noncommutativity

Classical and quantum bicosmology with noncommutativity

Thermal properties of a two-dimensional Duffin-Kemmer-Petiau oscillator under an external magnetic field in the presence of a minimal length

Klein-Gordon Oscillator In Dynamical Noncommutative Space

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