Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2001.02850 · Physical review. D/Physical review. D.

Generalized uncertainty principle and point interaction

DaeKil Park, Eylee Jung

Published Mar 11, 2020• 13 citations
arXivHTMLPDF

Abstract

The nonrelativistic quantum mechanics with a generalized uncertainty principle (GUP) is examined when the potential is a one-dimensional $\ensuremath{\delta}$-function. It is shown that unlike usual quantum mechanics, the Schr\"odinger and Feynman's path-integral approaches are inequivalent at the first order of the GUP parameter.

DOI
10.1103/physrevd.101.066007

Related papers

Generalized uncertainty principle and d -dimensional quantum mechanics

DaeKil Park

Nonrelativistic quantum mechanics with a generalized uncertainty principle (GUP) is examined in $d$-dimensional free particle and harmonic oscillator systems. The Feynman propagators for these systems are exactly derived within the first order of the GUP parameter.

arXiv:2003.13856•Physical review. D/Physical review. D.•May 13, 2020•10 citations

Path integral for nonrelativistic generalized uncertainty principle corrected Hamiltonian

Sudipta Das, Souvik Pramanik

The generalized uncertainty principle (GUP) has brought the idea of the existence of a minimum measurable length in quantum physics. Depending on this GUP, the nonrelativistic Hamiltonian at the Planck scale is modified. In this paper, we construct the kernel for this GUP-corrected Hamiltonian for a free particle by applying the Hamiltonian path integral approach and checking the validity conditions for this kernel thoroughly. Interestingly, the probabilistic interpretation of this kernel induces a momentum upper bound in the theory which is comparable with GUP-induced maximum momentum uncertainty.

arXiv:1205.3919•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Oct 1, 2012•28 citations

Feynman Propagator of the Arthurs-Kelly system at the Planck Scale

Mi-Ra Hwang, Eylee Jung, MuSeong Kim +1 more

The non-relativistic quantum mechanics with a generalized uncertainty principle (GUP) is examined in the Arthurs-Kelly system. The Feynman propagator for this system is exactly derived within the first order of the GUP parameter $β$. The application of it in the early universe stage is briefly discussed.

arXiv:2503.09111•Mar 12, 2025•0 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:1702.03498•Feb 12, 2017•0 citations

Generalized uncertainty principle and its implications on geometric phases in quantum mechanics

Giuseppe Gaetano Luciano, Luciano Petruzziello

Abstract We study the implications of the generalized uncertainty principle (GUP) with a minimal measurable length on some quantum mechanical interferometry phenomena, such as the Aharonov–Bohm, Aharonov–Casher, COW and Sagnac effects. By resorting to a modified Schrödinger equation, we evaluate the lowest-order correction to the phase shift of the interference pattern within two different GUP frameworks: the first one is characterized by the redefinition of the physical momentum only, and the other is a Lorentz covariant GUP which also predicts non-commutativity of spacetime. The obtained results allow us to fix upper bounds on the GUP deformation parameters which may be tested through future high-precision interferometry experiments.

The European Physical Journal Plus•Feb 1, 2021•38 citations

A framework for nonrelativistic isotropic models based on generalized uncertainty principles

André Herkenhoff Gomes

Abstract The existence of a fundamental length scale in nature is a common prediction of distinct quantum gravity models. Discovery of such would profoundly change current knowledge of quantum phenomena and modifications to the Heisenberg uncertainty principle may be expected. Despite the attention given to this possibility in the past decades, there has been no common framework for a systematic investigation of so-called generalized uncertainty principles (GUP). In this work we provide such a framework in the context of nonrelativistic quantum mechanics. Our approach is based on very few assumptions: there is a fundamental length scale, space isotropy, invariance under parity and time reversal transformations, and symmetricity of the position and momentum operators. We show that simple dimensional analysis allows building a common framework for isotropic models based on GUP (we call those iGUP models). We discuss some popular GUP models in this context after elaborating on relevant theoretical aspects of the framework. At last, we translate current bounds on three often investigated GUP models into bounds on parameters of such common iGUP framework.

arXiv:2202.02044•Journal of Physics A Mathematical and Theoretical•Jan 20, 2023•8 citations
The nonrelativistic quantum mechanics with a generalized uncertainty principle (GUP) is examined when the potential is a one-dimensional \ensuremathδ\ensuremath{\delta}\ensuremathδ-function. It is shown that unlike usual quantum mechanics, the Schr"odinger and Feynman's path-integral approaches are inequivalent at the first order of the GUP parameter.
Nonrelativistic quantum mechanics with a generalized uncertainty principle (GUP) is examined in ddd-dimensional free particle and harmonic oscillator systems. The Feynman propagators for these systems are exactly derived within the first order of the GUP parameter.
The generalized uncertainty principle (GUP) has brought the idea of the existence of a minimum measurable length in quantum physics. Depending on this GUP, the nonrelativistic Hamiltonian at the Planck scale is modified. In this paper, we construct the kernel for this GUP-corrected Hamiltonian for a free particle by applying the Hamiltonian path integral approach and checking the validity conditions for this kernel thoroughly. Interestingly, the probabilistic interpretation of this kernel induces a momentum upper bound in the theory which is comparable with GUP-induced maximum momentum uncertainty.
The non-relativistic quantum mechanics with a generalized uncertainty principle (GUP) is examined in the Arthurs-Kelly system. The Feynman propagator for this system is exactly derived within the first order of the GUP parameter βββ. The application of it in the early universe stage is briefly discussed.
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.
Abstract We study the implications of the generalized uncertainty principle (GUP) with a minimal measurable length on some quantum mechanical interferometry phenomena, such as the Aharonov–Bohm, Aharonov–Casher, COW and Sagnac effects. By resorting to a modified Schrödinger equation, we evaluate the lowest-order correction to the phase shift of the interference pattern within two different GUP frameworks: the first one is characterized by the redefinition of the physical momentum only, and the other is a Lorentz covariant GUP which also predicts non-commutativity of spacetime. The obtained results allow us to fix upper bounds on the GUP deformation parameters which may be tested through future high-precision interferometry experiments.
Abstract The existence of a fundamental length scale in nature is a common prediction of distinct quantum gravity models. Discovery of such would profoundly change current knowledge of quantum phenomena and modifications to the Heisenberg uncertainty principle may be expected. Despite the attention given to this possibility in the past decades, there has been no common framework for a systematic investigation of so-called generalized uncertainty principles (GUP). In this work we provide such a framework in the context of nonrelativistic quantum mechanics. Our approach is based on very few assumptions: there is a fundamental length scale, space isotropy, invariance under parity and time reversal transformations, and symmetricity of the position and momentum operators. We show that simple dimensional analysis allows building a common framework for isotropic models based on GUP (we call those iGUP models). We discuss some popular GUP models in this context after elaborating on relevant theoretical aspects of the framework. At last, we translate current bounds on three often investigated GUP models into bounds on parameters of such common iGUP framework.