The Generalized Uncertainty Principle and Harmonic Interaction in Three Spatial Dimensions

Hassanabadi, H.; Hooshmand, Parisa; Zarrinkamar, S.

doi:10.1007/s00601-014-0910-7

Cited by 22 publications

(5 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This equation was also encountered by Hassanabadi, Hooshmand, and Zarrinkamar [14] in their analysis of the same problem. In this work, we present an exact solution to the Duffing equation in terms of elliptic functions.…”

Section: Harmonic Oscillatorsupporting

confidence: 55%

Exactly Solvable Dynamical Models with a Minimal Length Uncertainty

Bernardo

Esguerra

2015

Few-Body Syst

View full text Add to dashboard Cite

We present exact analytical solutions to the classical equations of motion and analyze the dynamical consequences of the existence of a minimal length for the free particle, particle in a linear potential, anti-symmetric constant force oscillator, harmonic oscillator, vertical harmonic oscillator, linear diatomic chain, and linear triatomic chain. It turns out that a minimal length increases the speed of a free particle and the rate of fall of a particle that is subject to the influence of a linear potential. Our results suggest that the characteristic frequency of systems tend to increase when there is a minimal length. This is a common feature that we observed for the oscillator systems that we have considered.

show abstract

Section: Harmonic Oscillatorsupporting

confidence: 55%

Exactly Solvable Dynamical Models with a Minimal Length Uncertainty

Bernardo

Esguerra

2015

Few-Body Syst

View full text Add to dashboard Cite

show abstract

“…In this section, we would like to obtain Heisenberg algebra by considering a harmonic oscillator potential [30,31]. Therefore, we consider the following modified (anti)-de Sitter models a…”

Section: Heisenberg Algebra For Harmonic Oscillator By Modified (Anti...mentioning

confidence: 99%

“…On the other hand, using the expansion for wt cos 3 ( ) term, we obtain the deformed frequency [30,32] as…”

mentioning

confidence: 99%

Investigation of Heisenberg algebra for a modified anti-de Sitter and modified anti-Snyder models

Farahani¹,

Hassanabadi

Chung

et al. 2020

Commun. Theor. Phys.

View full text Add to dashboard Cite

In this paper, we consider a possible modification of the de Sitter and anti-de Sitter space for the extended uncertainty principle. For the modified anti-de Sitter model we discuss the representation and wave functions of the momentum operator for a one-dimensional box problem. Also, we consider modified Snyder and anti-Snyder models for the generalized uncertainty principle. Then, we assume the Hamiltonian with different potential and solve the Heisenberg algebra for the modified (anti)-de Sitter and (anti)-Snyder models in both position and in the momentum space.

show abstract

“…This generalization, on the other hand, would imply in the modification of the properties of the quantum system under consideration, namely the eigenfunctions and the eigenvalues. This is the main reason why recent works on the so-called Minimal Length Quantum Mechanics (MLQM) has underwent a vertiginous growth [17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47].…”

Section: Introductionmentioning

confidence: 99%

Generalized relativistic harmonic oscillator in minimal length quantum mechanics

Castro¹,

Obispo²

2017

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

Abstract. We solve the generalized relativistic harmonic oscillator in 1 + 1 dimensions in the presence of a minimal length. Using the momentum space representation, we explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. Furthermore, we also find an isolated solution from the Sturm-Liouville scheme. All cases already analyzed in the literature, are obtained as particular cases.

show abstract

The Generalized Uncertainty Principle and Harmonic Interaction in Three Spatial Dimensions

Cited by 22 publications

References 34 publications

Exactly Solvable Dynamical Models with a Minimal Length Uncertainty

Exactly Solvable Dynamical Models with a Minimal Length Uncertainty

Investigation of Heisenberg algebra for a modified anti-de Sitter and modified anti-Snyder models

Generalized relativistic harmonic oscillator in minimal length quantum mechanics

Contact Info

Product

Resources

About