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We find exact energy eigenvalues and eigenfunctions of the quantum bouncer in the presence of the minimal length uncertainty and the maximal momentum. This form of Generalized (Gravitational) Uncertainty Principle (GUP) agrees with various…

Various theories of quantum gravity predict the existence of a minimum length scale, which leads to the modification of the standard uncertainty principle to the Generalized Uncertainty Principle (GUP). In this paper, we study two forms of…

In a recent paper, we presented a nonperturbative higher order generalized uncertainty principle (GUP) that is consistent with various proposals of quantum gravity such as string theory, loop quantum gravity, doubly special relativity, and…

We present exact energy spectrum and eigenfunctions of the one-dimensional hydrogen atom in the presence of the minimal length uncertainty. By requiring the self-adjointness property of the Hamiltonian, we completely determine the…

We present a higher order generalized (gravitational) uncertainty principle (GUP) in the form $[X,P]=i\hbar/(1-\beta P^2)$. This form of GUP is consistent with various proposals of quantum gravity such as string theory, loop quantum…

This paper provides a concise overview of the comprehensive version of the Generalized Uncertainty Principle (GUP) derived from nonlocal quantum mechanics and extensively addressed by S. Masood, et al. We utilize the specific constraint of…

Different candidates of Quantum Gravity such as String Theory, Doubly Special Relativity, Loop Quantum Gravity and black hole physics all predict the existence of a minimum observable length or a maximum observable momentum which modifies…

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…

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…

The prediction of a minimal length scale by various quantum gravity candidates (such as string/M theory, Doubly Special Relativity, Loop Quantum Gravity and others) have suggested modification of Heisenberg Uncertainty Principle (HUP),…

Various approaches to Quantum Gravity (such as String Theory and Doubly Special Relativity), as well as black hole physics predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg…

Based on the doubly special relativity we find a new type of generalized uncertainty principle (GUP) where the coordinate remain unaltered at the high energy while the momentum is deformed at the high energy so that it may be bounded from…

String theory, quantum geometry, loop quantum gravity and black hole physics all indicate the existence of a minimal observable length on the order of Planck length. This feature leads to a modification of Heisenberg uncertainty principle.…

The existence of a minimum observable length and/or a maximum observable momentum is in agreement with various candidates of quantum gravity such as string theory, loop quantum gravity, doubly special relativity and black hole physics. In…

One can use the generalized uncertainty principle (GUP) to incorporate the minimum measurable length in quantum gravity. It may be interesting to have a minimal time interval as well as the minimal length in the relativistic version of…

We review highlights from string theory, black hole physics and doubly special relativity and some "thought" experiments which were suggested to probe the shortest distance and/or the maximum momentum at the Planck scale. The models which…

We present a novel generalization of the Heisenberg uncertainty principle which introduces the existence of a maximal observable momentum and at the same time does not entail a minimal indeterminacy in position. The above result is an exact…

We present the energy eigenvalues of a quantum bouncer in the framework of the Generalized (Gravitational) Uncertainty Principle (GUP) via quantum mechanical and semiclassical schemes. In this paper, we use two equivalent nonperturbative…

The Generalized Uncertainty Principle (GUP) naturally emerges in several quantum gravity models, predicting the existence of a minimal length at Planck scale. Here, we consider the quadratic GUP as a semiclassical approach to thermodynamic…

The Generalized Uncertainty Principle (GUP) extends the Heisenberg Uncertainty Principle (HUP) by suggesting a minimum observable scale that includes the effects of quantum gravity, which is supposed to potentially result in observable…