A Class of Gup Solutions in Deformed Quantum Mechanics

Pedram, Pouria

doi:10.1142/s0218271810018153

Cited by 71 publications

(52 citation statements)

References 28 publications

(19 reference statements)

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“…¼ hPi 2 . As Kempf, Mangano, and Mann have suggested in their seminal paper, in momentum space representation, we can write X and P as [35] PðpÞ ¼ pðpÞ;…”

Section: The Generalized Uncertainty Principlementioning

confidence: 99%

“…In this representation the position operator is merely symmetric, but P is self-adjoint [35]. With this definition, the commutation relation (2) is exactly satisfied.…”

Section: The Generalized Uncertainty Principlementioning

confidence: 99%

“…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%

See 2 more Smart Citations

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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“…¼ hPi 2 . As Kempf, Mangano, and Mann have suggested in their seminal paper, in momentum space representation, we can write X and P as [35] PðpÞ ¼ pðpÞ;…”

Section: The Generalized Uncertainty Principlementioning

confidence: 99%

“…In this representation the position operator is merely symmetric, but P is self-adjoint [35]. With this definition, the commutation relation (2) is exactly satisfied.…”

Section: The Generalized Uncertainty Principlementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

New approach to nonperturbative quantum mechanics with minimal length uncertainty

2012

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“…But the story is changed by considering the modified uncertainty principle due to the quantum gravity which is now called the Generalized Uncertainty Principle (GUP). In fact, due to the non-zero effective cutoff, it is not possible to set (∆x) min = 0 whenever the effects of quantum gravity become important meaning that we should replace HUP by GUP [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

A note on coherent states with quantum gravity effects

Sadeghnezhad¹

2016

Chinese Journal of Physics

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Existence of a minimal measurable length and an upper bound for the momentum fluctuations are the casting reasons for generalization of uncertainty principle and then reformulation of Hilbert space representation of quantum mechanics. In this paper, we study the consequences of the Generalized Uncertainty Principle (GUP) in the presence of both minimal length and maximal momentum. We consider a simple harmonic oscillator in the framework of GUP by introducing it's energy eigenstates and energy spectrum.Investigation of coherent states for a generalized harmonic oscillator and it's generic behavior are the other topics in our study. 04.60.Bc PACS

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“…Since in the GUP framework one cannot probe distances smaller than the minimum measurable length at a nite time, we expect it modies the Hamiltonian of physical systems, too (see [5] for instance). Recently, a GUP is proposed by Ali et al which is consistent with the existence of the minimal measurable length and the maximal measurable momentum [14,15].…”

Section: Introductionmentioning

confidence: 99%