Modern Physics Letters A

The generalized uncertainty principle from the doubly special relativity: Algebraic approach, Ramsauer effect and delta potential

Won Sang Chung, HASSAN HASSANABADI, Min Su Kang, Hee Hun Sung, Jinyeob Maeng, Seunghyun Lee, Young Il Moon

Published Mar 1, 2019• 12 citations

Abstract

In this paper, we consider the DSR-GUP which was first proposed by two of us [W. S. Chung and H. Hassanabadi, Phys. Lett. B 785, 127 (2018)]. Here, we introduce the deformed derivative corresponding to DSR-GUP to discuss the quantum mechanics based on DSR-GUP in an algebraical way. We use the deformed Fourier transform and its inverse transform to discuss the plane wave in [Formula: see text]-space and Gaussian packet. We also extend our discussion to the (1 + 1)-dimensional case. As examples, we discuss the Ramsauer–Townsend effect and delta potential.

DOI: 10.1142/s0217732319500524

Related papers

Generalized uncertainty principle from deformed angular momentum algebra

Ahmad Adel Abutaleb

This work establishes a link between deformed angular momentum operators and modifications of the quantum uncertainty principle. Starting from an algebra in which the standard angular momentum operators are deformed by two parameters, [Formula: see text] and [Formula: see text], we construct the corresponding momentum operators via [Formula: see text] where the radial operator [Formula: see text] is determined by the requirement that the standard momentum operator is recovered in the limit [Formula: see text], [Formula: see text]. The resulting commutation relations take the form [Formula: see text] where [Formula: see text] is a position-dependent deformation matrix. This leads to an uncertainty relation [Formula: see text] which is state-dependent, anisotropic and position-dependent. We use the term Generalized Uncertainty Principle (GUP) in its broad sense referring to any modification of the Heisenberg relation motivated by quantum-gravity ideas. However, the model does not yield a fixed minimal length of the kind familiar from conventional GUP models (e.g. [Formula: see text]). In the isotropic, limit the trace of the deformation matrix simplifies the bound to [Formula: see text] which can be considered as a rescaling of the uncertainty constant. Our work thus provides a geometric origin for modified uncertainty relations from symmetry breaking in the rotation group, and offers a framework in which quantum-gravity effects manifest themselves through state- and direction-dependent measurement limits, without necessarily introducing a universal minimal length.

International Journal of Modern Physics DMar 13, 20260 citations

One-dimension quantum systems in the framework of the most general deformation GUP form

Ying-Jie Zhao, Ji, Yan-Fang, Yao, Guang-Rui +2 more

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 this GUP formulation to compute the energy correction and the modified wave function for the linear potential in one dimension. In addition, we examine the impact of deformation on a one-dimensional delta potential well and a one-dimensional delta potential barrier. Furthermore, we specifically focus on the impact of deformation on hydrogen atoms existing in one dimension, and we conduct a distinct investigation into the Stark effect on the atom.

arXiv:1702.03498Feb 12, 20170 citations

Factorization in the quantum mechanics with the generalized uncertainty principle

Won Sang Chung

In this paper, we discuss the quantum mechanics with the generalized uncertainty principle (GUP) where the commutation relation is given by [Formula: see text]. For this algebra, we obtain the eigenfunction of the momentum operator. We also study the GUP corrected quantum particle in a box. Finally, we apply the factorization method to the harmonic oscillator in the presence of a minimal observable length and obtain the energy eigenvalues by applying the perturbation method.

Modern Physics Letters AJul 6, 20150 citations

Unitary equivalence in generalized uncertainty principle theories

Sebastiano Segreto, Matteo Bruno

We analyze the issue of unitary equivalence within Generalized Uncertainty Principle (GUP) theories in the one-dimensional case. For a deformed Heisenberg algebra, its representation in terms of Hilbert space and conjugate operators is not uniquely determined, raising the question of whether different realizations of the same algebra are equivalent and describe the same physics. After proposing a definition of a quantum GUP theory, we establish conditions for unitary equivalence. Using this framework, we rigorously prove that two commonly used representations are unitarily equivalent, specifying the conditions under which this equivalence holds. We demonstrate this equivalence explicitly by providing a unitary map and showing how both GUP formulations yield the same physical results in two examples: the quantum harmonic oscillator and a free-falling particle. Finally, we discuss a case where equivalence fails, suggesting that a generalization of the Stone-von Neumann theorem may not be possible within the GUP framework under our definition of unitary equivalence.

arXiv:2509.05477Nuclear Physics BJan 3, 20261 citation

Step potential and Ramsauer-Townsend effect in Wigner-Dunkl quantum mechanics

Ali Askari, HASSAN HASSANABADI, Won Sang Chung

In this paper the continuity equation for Wigner-Dunkl-Schrodinger equation is studied. Some properties of ¨ ν-deformed functions related to Dunkl derivative are also studied. Based on these, the step potential and Ramsauer-Townsend effect are discussed in Wigner-Dunkl quantum mechanics

Revista Mexicana de FísicaJan 3, 20230 citations

The generalised uncertainty principle from a momentum-dependent translation operator

A. I. P Pires, J. P. M Braga, R. N. Costa Filho

A momentum-dependent translation operator, inspired by the position-dependent translation operator (PDTO) framework, is introduced to describe a particle in a minimum-length scenario. We show that a chosen momentum-dependent translation profile G ( p ) induces a deformed commutation relation between position and momentum and the corresponding Generalized Uncertainty Principle (GUP), providing a structural construction rather than postulating the commutator independently. The construction is the momentum-space dual of the position-space operator that yields the Extended Uncertainty Principle, so that EUP and GUP emerge as the two faces of a single translation principle. We then adapt the split-operator method, using the eigenfunctions of the momentum operator modulated by a Gaussian in the representation of Brau and Pedram, to describe a particle under three potentials: free, linear, and quadratic. In all cases the quantum mean values track the classical dynamics obtained from the modified Poisson brackets, with a leading correction proportional to β ⟨ p ⟩(Δ p ) 2 that we identify analytically. Propagating a classical ensemble with the same initial spread shows this correction to be statistical rather than quantum: it is reproduced to machine precision for free and linear forces, and the genuinely quantum residue in the oscillator amounts to 5 × 10 − 5 of the amplitude. We also bound the error of the first-order truncation by comparison with the exact tangent Hamiltonian. This places the deformed quantum–classical correspondence on a quantitative footing, complementing earlier work on coherent states and on packet dispersion in a minimum-length scenario.

Physics Letters BOct 14, 20260 citations