Ground State of the Hydrogen Atom via Dirac Equation in a Minimal Length Scenario

Abstract

In this work we calculate the correction to the ground state energy of the hydrogen atom due to contributions arising from the presence of a minimal length. The minimal length scenario is introduced by means of modifying the Dirac equation through a deformed Heisenberg algebra (kempf algebra). With the introduction of the Coulomb potential in the new Dirac energy operator, we calculate the energy shift of the ground state of the hydrogen atom in first order of the parameter related to the minimal length via perturbation theory.

11 pages

References in corpus (17)

• The Hierarchy Problem and New Dimensions at a Millimeter
• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Bounds on Universal Extra Dimensions
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Minimal Length Scale Scenarios for Quantum Gravity
• Nonpointlike Particles in Harmonic Oscillators
• Minimal Length Uncertainty Relation and Ultraviolet Regularisation
• Improved Measurement of the Hydrogen 1S - 2S Transition Frequency
• Minimal Length Uncertainty Relation and Hydrogen Atom
• Signatures in the Planck Regime
• Hydrogen-atom spectrum under a minimal-length hypothesis
• Self-consistency in Theories with a Minimal Length
• Minimal Length Uncertainty Relation and the Hydrogen Spectrum
• Physics on Smallest Scales - An Introduction to Minimal Length Phenomenology
• Hydrogen atom in momentum space with a minimal length
• Maximally Localized States in Quantum Mechanics with a Modified Commutation Relation to All Orders
• Coulomb potential in one dimension with minimal length: A path integral approach

Cited by in corpus (13)

• GUP Modified Hawking Radiation in Bumblebee Gravity
• Remnants, fermions' tunnelling and effects of quantum gravity
• 30 years in: Quo vadis generalized uncertainty principle?
• Generalized uncertainty principle or curved momentum space?
• Kratzer's molecular potential in quantum mechanics with a generalized uncertainty principle
• Quantum-spacetime effects on nonrelativistic Schrödinger evolution
• Pseudoharmonic oscillator in quantum mechanics with a minimal length
• The Harmonic Oscillator in the Classical Limit of a Minimal-Length Scenario
• Dirac $\delta$-function potential in quasiposition representation of a minimal-length scenario
• Two-body Dirac equation in DSR: results for fermion-antifermion pairs
• Relativistic Approach to the Hydrogen Atom in a Minimal Length Scenario
• Effects of Extended Uncertainty Principle on the Relativistic Coulomb Potential
• Towards quantum Mechanics on the curved cotangent bundle