Hydrogen atom in momentum space with a minimal length

Bouaziz, Djamil; Ferkous, N.

doi:10.1103/physreva.82.022105

Cited by 67 publications

(66 citation statements)

References 33 publications

(91 reference statements)

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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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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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“…Alternatively, one may use the requirement of single-valuedness of eigenfunctions (24) to find the quantization condition which leads to…”

Section: Single-valuedness Criteriamentioning

confidence: 99%

“…In the presence of the minimal length uncertainty, this problem is also studied exactly and perturbatively in Refs. [23][24][25][26][27]. Moreover, using the formally self-adjoint representation [28,29], the quantization condition is completely determined in one-dimension upon imposing the Hermicity condition on the GUP-corrected Hamiltonian [30].…”

Section: Introductionmentioning

confidence: 99%

One-dimensional hydrogen atom with minimal length uncertainty and maximal momentum

Pedram¹

2013

EPL

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Abstract. We present exact energy eigenvalues and eigenfunctions of the onedimensional hydrogen atom in the framework of the Generalized (Gravitational) Uncertainty Principle (GUP). This form of GUP is consistent with various theories of quantum gravity such as string theory, loop quantum gravity, black-hole physics, and doubly special relativity and implies a minimal length uncertainty and a maximal momentum. We show that the quantized energy spectrum exactly agrees with the semiclassical results.

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“…The effects of quantum gravity on compact star cores and on the Planck era of the universe were discussed in the papers [61,62,63,64]. The treatment of hydrogen atom problems with a generalized uncertainty relation was present in the work of Bouaziz et al [65,66,67]. Incorporating the GUP into black holes, the thermodynamical properties and the remnants were studied in recent researches [68,69,70,71,72,73,74].…”

Section: Introductionmentioning

confidence: 99%

Effects of quantum gravity on black holes

Chen

Yang

et al. 2014

Int. J. Mod. Phys. A

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In this review, we discuss effects of quantum gravity on black hole physics. After a brief review of the origin of the minimal observable length from various quantum gravity theories, we present the tunneling method. To incorporate quantum gravity effects, we modify the Klein-Gordon equation and Dirac equation by the modified fundamental commutation relations. Then we use the modified equations to discuss the tunneling radiation of scalar particles and fermions. The corrected Hawking temperatures are related to the quantum numbers of the emitted particles. Quantum gravity corrections slow down the increase of the temperatures. The remnants are observed as M Res. The mass is quantized by the modified Wheeler-DeWitt equation and is proportional to n in quantum gravity regime. The thermodynamical property of the black hole is studied by the influence of quantum gravity effects.

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Hydrogen atom in momentum space with a minimal length

Cited by 67 publications

References 33 publications

Influence of a minimal length on the creation of scalar particles

Influence of a minimal length on the creation of scalar particles

One-dimensional hydrogen atom with minimal length uncertainty and maximal momentum

Effects of quantum gravity on black holes

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