Related papers: Dimensionality as a Perturbation Parameter in the …
This paper presents a comprehensive analysis of the generalized radial uncertainty product for the d-dimensional non-relativistic Hydrogen atom in position space. Utilizing the framework of quantum mechanics in d-dimensional spherical…
There has been disagreement in the literature on whether the hydrogen atom spectrum receives any tree-level correction due to noncommutativity. Here we shall clarify the issue and show that indeed a general argument on the structure of…
It is shown that, Baire generically, the bound states of the Hamiltonian of the Hydrogen atom have spectral measures with exact $0$-lower and $1/3$-upper generalized fractal dimensions; the relation to (a weak form of) dynamical…
Modifications of Heisenberg's uncertainty relations have been proposed in the literature which imply a minimum position uncertainty. We study the low energy effects of the new physics responsible for this by examining the consequent change…
We study the corrections to the fine-structure constant from the generalized uncertainty principle in the spacetime of a domain wall. We also calculate the corrections to the standard formula to the energy of the electron in the hydrogen…
We study energy spectrum for hydrogen atom with deformed Heisenberg algebra leading to minimal length. We develop correct perturbation theory free of divergences. It gives a possibility to calculate analytically in the 3D case the…
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…
The hydrogen atom is supposed to be described by a generalization of Schr\"{o}dinger equation, in which the Hamiltonian depends on an iterated Laplacian and a Coulomb-like potential $r^{-\beta}$. Starting from previously obtained solutions…
The nonrelativistic hydrogen atom in $D=3-2\epsilon$ dimensions is the reference system for perturbative schemes used in dimensionally regularized nonrelativistic effective field theories to describe hydrogen-like atoms. Solutions to the…
Various models of quantum gravity suggest a modification of the Heisenberg's Uncertainty Principle, to the so-called Generalized Uncertainty Principle, between position and momentum. In this work we show how this modification influences the…
We consider Uncertainty Principles which take into account the role of gravity and the possible existence of extra spatial dimensions. Explicit expressions for such Generalized Uncertainty Principles in 4+n dimensions are given and their…
The question of whether hydrogen atoms can exist or not in spaces with a number of dimensions greater than 3 is revisited, considering higher dimensional Euclidean spaces. Previous results which lead to different answers to this question…
A good generalization of the Euclidean dimension to disordered systems and non crystalline structures is commonly required to be related to large scale geometry and it is expected to be independent of local geometrical modifications. The…
This chapter explores the notion of "dimension" of a set. Various power laws by which an Euclidean space can be characterized are used to define dimensions, which then explore different aspects of the set. Also discussed are the…
Motivated by recent works, we employ the bounds on the dimensionless quantum-gravity parameter obtained from six gravitational tests in order to obtain bounds on the dimensionless parameter of the generalized uncertainty principle with…
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…
Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system can we simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time.…
In this article we examine a Generalized Uncertainty Principle which differs from the Heisenberg Uncertainty Principle by terms linear and quadratic in particle momenta, as proposed by the authors in an earlier paper. We show that this…
The statistical model of the hadron as a quarkonium system suggests the dimensional dependence of some of the properties of the hadron like the scaling in its probability density with the anomalous dimension as the exponent,the…
We develop a mathematical formalism that allows to study decoherence with a great level generality, so as to make it appear as a geometrical phenomenon between reservoirs of dimensions. It enables us to give quantitative estimates of the…