One-dimensional Coulomb-like problem in deformed space with minimal length

Fityo, T.V.; Vakarchuk, I. O.; Tkachuk, V. M.

doi:10.1088/0305-4470/39/9/010

Cited by 84 publications

(102 citation statements)

References 23 publications

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“…The wave functions and the corresponding energy levels are obtained. The leading correction to the energy spectrum is proportional to √ β, which is in agreement with that of the one-dimensional case [21]. The dependence on √ β drastically lowers the minimal length scale, which is of about 10 −9 fm.…”

Section: Discussionsupporting

confidence: 86%

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Hydrogen atom in momentum space with a minimal length

Bouaziz

Ferkous

2010

Phys. Rev. A

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A momentum representation treatment of the hydrogen atom problem with a generalized uncertainty relation,which leads to a minimal length (∆X i ) min = √ 3β + β ′ , is presented. We show that the distance squared operator can be factorized in the case β ′ = 2β. We analytically solve the s-wave bound-state equation. The leading correction to the energy spectrum caused by the minimal length depends on √ β. An upper bound for the minimal length is found to be about 10 −9fm. * Electronic address: djamilbouaziz@mail.univ-jijel.dz

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Section: Discussionsupporting

confidence: 86%

“…As we see, our result coincides with that of the one-dimensional Coulomb potential [21], where the quantization condition has been derived by imposing the Hermiticity of the Hamiltonian.…”

Section: Momentum Space Treatmentsupporting

confidence: 82%

Hydrogen atom in momentum space with a minimal length

Bouaziz

Ferkous

2010

Phys. Rev. A

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“…This explains why various physical problems are reconsidered by taking into account the minimal length. As example, we cite the harmonic oscillator [24][25][26], the Hydrogen atom [26][27][28][29][30][31][32], the inverse square potential [33], the Dirac oscillator [34], and the resonant scattering by a potential barrier [35,36]. Elsewhere, the influence of the minimal length on the Casimir effect has been communicated in several works [37,38].…”

Section: Introductionmentioning

confidence: 99%

Influence of a minimal length on the creation of scalar particles

Haouat

Nouicer

2014

Phys. Rev. D

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In this paper we have studied the problem of scalar particles pair creation by an electric field in the presence of a minimal length. Two sets of exact solutions for the Klein Gordon equation are given in momentum space. Then the canonical method based on Bogoliubov transformation connecting the "in" with the "out" states is applied to calculate the probability to create a pair of particles and the mean number of created particles. The number of created particles per unit of time per unit of length, which is related directly to the experimental measurements, is calculated. It is shown that, with an electric field less than the critical value, the minimal length minimizes the particle creation. It is shown, also, that the limit of zero minimal length reproduces the known results corresponding to the ordinary quantum fields.

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“…This expression was successfully used to consider onedimensional Coulomb-like problem [9]. Parameter δ depends on boundary conditions: for smooth potentials and deformation function f (P ) such that f (0) = 0 it equals 1/2.…”

Section: Introductionmentioning

confidence: 99%