Some aspects of gravitational quantum mechanics

Nozari, Kourosh; Azizi, Tahereh

doi:10.1007/s10714-006-0262-9

Cited by 110 publications

(85 citation statements)

References 35 publications

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“…This assumption is not unjustifiable in view of the fact that the standard model charges cannot move in extra dimensions in theory of brane world model. Now, extra dimensions are widely accepted by theorists and there are large works about it [7][8][9][10][11][12][13]. This model gives us the new spectra, which looks same as our previous works [6], however, have different physical meaning.…”

Section: Introductionsupporting

confidence: 54%

Spectra of Hydrogen Atom with GUP and Extra Dimensions

Mu¹

2013

JMP

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We argue that the Generalized Uncertainty Ptinciple (GUP) and the compact Extra dimensions will lead the hydrogen atom has the non bounded state spectra which equal the free particle in extra dimensions. We use Generalized Uncertainty Principle (GUP) to calculate the new energy spectra of hydrogen atom, and which lives in three dimensional Euclidean spaces with one extra dimension. The result is not familiar with our known before that when n is large enough. In our modified new spectra, we obtain that, which is lager than zero.These new spectra give us new method to obtain the existence of extra dimensions. Finally, we find that the spectra are same as part of extra dimensions in planck scale.

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Section: Introductionsupporting

confidence: 54%

Spectra of Hydrogen Atom with GUP and Extra Dimensions

Mu¹

2013

JMP

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“…Indeed, the notion of minimal length should quantum mechanically be described as a minimal uncertainty in position measurements. The introduction of this idea has drawn much attention in recent years and many papers have been appeared in the literature to address the effects of GUP on various quantum mechanical systems and phenomena [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]35,36].…”

Section: Introductionmentioning

confidence: 99%

New approach to nonperturbative quantum mechanics with minimal length uncertainty

2012

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The existence of a minimal measurable length is a common feature of various approaches to quantum gravity such as string theory, loop quantum gravity, and black-hole physics. In this scenario, all commutation relations are modified and the Heisenberg uncertainty principle is changed to the so-called Generalized (Gravitational) Uncertainty Principle (GUP). Here, we present a one-dimensional nonperturbative approach to quantum mechanics with minimal length uncertainty relation which implies X ¼ x to all orders and P ¼ p þ 1 3 p 3 to first order of GUP parameter , where X and P are the generalized position and momentum operators and ½x; p ¼ iℏ. We show that this formalism is an equivalent representation of the seminal proposal by Kempf, Mangano, and Mann and predicts the same physics. However, this proposal reveals many significant aspects of the generalized uncertainty principle in a simple and comprehensive form and the existence of a maximal canonical momentum is manifest through this representation. The problems of the free particle and the harmonic oscillator are exactly solved in this GUP framework and the effects of GUP on the thermodynamics of these systems are also presented. Although X, P, and the Hamiltonian of the harmonic oscillator all are formally selfadjoint, the careful study of the domains of these operators shows that only the momentum operator remains self-adjoint in the presence of the minimal length uncertainty. We finally discuss the difficulties with the definition of potentials with infinitely sharp boundaries.

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“…More general cases of such commutation relations are studied in [7]- [11]. Also various applications of the low energy effects of the modified Heisenberg uncertainty relations have been extensively studied, see for example [12]- [15]. In this letter we consider a two dimensional minisuperspace of Bianchi type I cosmology in the GUP framework.…”

Section: Introductionmentioning

confidence: 99%

Generalized uncertainty principle in Bianchi type I quantum cosmology

Vakili

Sepangi

2007

Physics Letters B

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We study a quantum Bianchi type I model in which the dynamical variables of the corresponding minisuperspace obey the generalized Heisenberg algebra. Such a generalized uncertainty principle has its origin in the existence of a minimal length suggested by quantum gravity and sting theory. We present approximate analytical solutions to the corresponding Wheeler-DeWitt equation in the limit where the scale factor of the universe is small and compare the results with the standard commutative and noncommutative quantum cosmology. Similarities and differences of these solutions are also discussed.

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Some aspects of gravitational quantum mechanics

Cited by 110 publications

References 35 publications

Spectra of Hydrogen Atom with GUP and Extra Dimensions

Spectra of Hydrogen Atom with GUP and Extra Dimensions

New approach to nonperturbative quantum mechanics with minimal length uncertainty

Generalized uncertainty principle in Bianchi type I quantum cosmology

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