Dirac -function potential in quasiposition representation of a minimal-length scenario
arXiv:1704.08236 · doi:10.1140/epjc/s10052-018-5659-6
Abstract
A minimal-length scenario can be considered as an effective description of quantum gravity effects. In quantum mechanics the introduction of a minimal length can be accomplished through a generalization of Heisenberg's uncertainty principle. In this scenario, state eigenvectors of the position operator are no longer physical states and the representation in momentum space or a representation in a quasiposition space must be used. In this work, we solve the Schroedinger equation with Dirac -function potential in quasiposition space. We calculate the bound state energy and the coefficients of reflection and transmission for scattering states. We show that leading corrections are of order of the minimal length $({\sl O}(\sqrtβ))$ and the coefficients of reflection and transmission are no longer the same for the Dirac delta well and barrier as in ordinary quantum mechanics. Furthermore, assuming that the equivalence of the 1s state energy of the hydrogen atom and the bound state energy of the Dirac -function potential in 1-dim is kept in a minimal-length scenario, we also find that the leading correction term for the ground state energy of the hydrogen atom is of order of the minimal length and m.
References in corpus (42)
- Hilbert Space Representation of the Minimal Length Uncertainty Relation
- Universality of Quantum Gravity Corrections
- Large momentum part of fermions with large scattering length
- Energetics of a strongly correlated Fermi gas
- The Casimir effect: Recent controversies and progress
- Nonpointlike Particles in Harmonic Oscillators
- Improved Measurement of the Hydrogen 1S - 2S Transition Frequency
- Minimal Length Uncertainty Relation and Hydrogen Atom
- Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
- Exact Solution of the Harmonic Oscillator in Arbitrary Dimensions with Minimal Length Uncertainty Relations
- Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
- Phenomenological Implications of the Generalized Uncertainty Principle
- Generalized Uncertainty Principle: Approaches and Applications
- Calculating Vacuum Energies in Renormalizable Quantum Field Theories: A New Approach to the Casimir Problem
- Dirac oscillator with nonzero minimal uncertainty in position
- Review on Generalized Uncertainty Principle
- Universal Properties of the Ultra-Cold Fermi Gas
- Hydrogen-atom spectrum under a minimal-length hypothesis
- Composite system in deformed space with minimal length
- Self-consistency in Theories with a Minimal Length
- Minimal Length Uncertainty Relation and the Hydrogen Spectrum
- Some Aspects of Minimal Length Quantum Mechanics
- New Approach to Nonperturbative Quantum Mechanics with Minimal Length Uncertainty
- Perturbation hydrogen-atom spectrum in deformed space with minimal length
- The Casimir Effect in the Presence of a Minimal Length
- Physics on Smallest Scales - An Introduction to Minimal Length Phenomenology
- Casimir Effect in the Presence of Minimal Lengths
- Harmonic oscillator with minimal length uncertainty relations and ladder operators
- The Casimir Effect in Minimal Length Theories based on a Generalized Uncertainity Principle
- Exact solutions of the (2+1) Dimensional Dirac equation in a constant magnetic field in the presence of a minimal length
- One dimensional Coulomb-like problem in deformed space with minimal length
- Minimal Length and Generalized Dirac Equation
- Hydrogen atom in momentum space with a minimal length
- Casimir-Polder intermolecular forces in minimal length theories
- Quantum Wells and the Generalized Uncertainty Principle
- Ground State of the Hydrogen Atom via Dirac Equation in a Minimal Length Scenario
- Quantum phase transitions of the Dirac oscillator in a minimal length scenario
- Maximally Localized States in Quantum Mechanics with a Modified Commutation Relation to All Orders
- Exactly solvable problems in the momentum space with a minimum uncertainty in position
- Coulomb potential in one dimension with minimal length: A path integral approach
- Less than perfect quantum wavefunctions in momentum-space: How phi(p) senses disturbances in the force
- Modification of the Casimir Effect due to a Minimal length scale