Related papers: Minimal Length and the Quantum Bouncer: A Nonpertu…
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…
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…
In this paper we study the effects of the Generalized Uncertainty Principle (GUP) on the spectrum of a particle that is bouncing vertically and elastically on a smooth reflecting floor in the Earth's gravitational field (a quantum bouncer).…
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…
We present exact energy eigenvalues and eigenfunctions of the one-dimensional hydrogen atom in the framework of the Generalized (Gravitational) Uncertainty Principle (GUP). This form of GUP is consistent with various theories of quantum…
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…
Various candidates of quantum gravity such as string theory, loop quantum gravity and black hole physics all predict the existence of a minimum observable length which modifies the Heisenberg uncertainty principle to so-called Generalized…
In this work, we point out an overlooked and subtle feature of the generalized uncertainty principle (GUP) approach to quantizing gravity: namely that different pairs of modified operators with the same modified commutator,…
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…
In the framework of the generalized uncertainty principle, the position and momentum operators obey the modified commutation relation $[X,P]=i\hbar\left(1+\beta P^2\right)$ where $\beta$ is the deformation parameter. Since the validity of…
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…
We present an exact treatment of the thermodynamics of physical systems in the framework of the generalized uncertainty principle (GUP). Our purpose is to study and compare the consequences of two GUPs that one implies a minimal length…
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…
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),…
We extend significantly previous works on the Hilbert space representations of the Generalized Uncertainty Principle (GUP) in 3+1 dimensions of the form $[X_i,P_j] = i F_{ij}$ where $ F_{ij} = f(P^2) \delta_{ij} + g(P^2) P_i P_j $ for any…
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…
The fundamental physical description of Nature is based on two mutually incompatible theories: Quantum Mechanics and General Relativity. Their unification in a theory of Quantum Gravity (QG) remains one of the main challenges of theoretical…
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.…
We present the coherent states of the harmonic oscillator 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…
A good hundred years after the necessity for a quantum theory of gravity was acknowledged by Albert Einstein, the search for it continues to be an ongoing endeavour. Nevertheless, the field still evolves rapidly as manifested by the recent…