Hydrogen atom in momentum space with a minimal length

Abstract

A momentum representation treatment of the hydrogen atom problem with a generalized uncertainty relation,which leads to a minimal length (ΔX_{i})_{min}= \hbar \sqrt(3β+β'), is presented. We show that the distance squared operator can be factorized in the case β'=2β. We analytically solve the s-wave bound-state equation. The leading correction to the energy spectrum caused by the minimal length depends on \sqrtβ. An upper bound for the minimal length is found to be about 10^{-9} fm.

10 pages

References in corpus (20)

• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Quantum gravity and minimum length
• Nonpointlike Particles in Harmonic Oscillators
• Minimal Length Uncertainty Relation and Hydrogen Atom
• Uncertainty Relation in Quantum Mechanics with Quantum Group Symmetry
• Exact Solution of the Harmonic Oscillator in Arbitrary Dimensions with Minimal Length Uncertainty Relations
• Short Distance vs. Long Distance Physics: The Classical Limit of the Minimal Length Uncertainty Relation
• Maximal Localisation in the Presence of Minimal Uncertainties in Positions and Momenta
• Hydrogen-atom spectrum under a minimal-length hypothesis
• Minimal Length Uncertainty Relation and gravitational quantum well
• Composite system in deformed space with minimal length
• Minimal Length Uncertainty Relation and the Hydrogen Spectrum
• Regularization of the Singular Inverse Square Potential in Quantum Mechanics with a Minimal length
• Perturbation hydrogen-atom spectrum in deformed space with minimal length
• The Casimir Effect in the Presence of a Minimal Length
• Casimir Effect in the Presence of Minimal Lengths
• Quantum Black Hole in the Generalized Uncertainty Principle Framework
• One dimensional Coulomb-like problem in deformed space with minimal length
• Corrections to the ns-levels of hydrogen atom in deformed space with minimal length
• Singular inverse square potential in arbitrary dimensions with a minimal length: Application to the motion of a dipole in a cosmic string background

Cited by in corpus (26)

• Minimal Length Scale Scenarios for Quantum Gravity
• Effects of quantum gravity on black holes
• 30 years in: Quo vadis generalized uncertainty principle?
• Generalized uncertainty principle or curved momentum space?
• On γ-rigid regime of the Bohr-Mottelson Hamiltonian in the presence of a minimal length
• Singular inverse square potential in coordinate space with a minimal length
• Kratzer's molecular potential in quantum mechanics with a generalized uncertainty principle
• One-dimensional hydrogen atom with minimal length uncertainty and maximal momentum
• Ground State of the Hydrogen Atom via Dirac Equation in a Minimal Length Scenario
• Influence of a Minimal Length on the Creation of Scalar Particles
• A note on the one-dimensional hydrogen atom with minimal length uncertainty
• The Constraints and Spectra of a Deformed Quantum Mechanics
• The quantum N-body problem with a minimal length
• Spectrum of the hydrogen atom in Snyder space in a semiclassical approximation
• Pseudoharmonic oscillator in quantum mechanics with a minimal length
• Dirac $\delta$-function potential in quasiposition representation of a minimal-length scenario
• A framework for nonrelativistic isotropic models based on generalized uncertainty principles
• Deformed Gazeau-Klauder Schrödinger-Cat States with Modified Commutation Relations
• Exactly solvable dynamical models with a minimal length uncertainty
• Relativistic Approach to the Hydrogen Atom in a Minimal Length Scenario
• Towards quantum Mechanics on the curved cotangent bundle
• Hartmann potential with a minimal length and generalized recurrence relations for matrix elements
• Non-Heisenbergian quantum mechanics
• Minimal length implications on the Hartree-Fock theory
• Deformed Heisenberg Algebra with a minimal length: Application to some molecular potentials
• Comment on "Cornell potential in generalized uncertainty principle formalism: the case of Schrödinger equation"