Harmonic oscillator with minimal length uncertainty relations and ladder operators

Abstract

We construct creation and annihilation operators for harmonic oscillators with minimal length uncertainty relations. We discuss a possible generalization to a large class of deformations of cannonical commutation relations. We also discuss dynamical symmetry of noncommutative harmonic oscillator.

8 pages, revtex4, final version, to appear in PRD

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Cited by in corpus (54)

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• Composite system in deformed space with minimal length
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• Formulation, Interpretation and Application of non-Commutative Quantum Mechanics
• Covariant realizations of kappa-deformed space
• Running Coupling with Minimal Length
• Quantum Black Hole in the Generalized Uncertainty Principle Framework
• Exact solutions of the (2+1) Dimensional Dirac equation in a constant magnetic field in the presence of a minimal length
• Effects of quantum gravity on black holes
• Modification of Heisenberg uncertainty relations in non-commutative Snyder space-time geometry
• Deformed Heisenberg algebra with minimal length and equivalence principle
• Harmonic oscillator with nonzero minimal uncertainties in both position and momentum in a SUSYQM framework
• More on a SUSYQM approach to the harmonic oscillator with nonzero minimal uncertainties in position and/or momentum
• Scattering problem in deformed space with minimal length
• Generalized kappa-deformed spaces, star-products, and their realizations
• Generalized uncertainty principle in Bianchi type I quantum cosmology
• Planck scale Corrections to the Harmonic Oscillator, Coherent and Squeezed States
• Exact solution of the Klein Gordon equation in the presence of a minimal length
• Noncommutative Differential Forms on the kappa-deformed Space
• Doubly Special Relativity in Position Space Starting from the Conformal Group
• Orbital magnetic moment of the electron in the hydrogen atom in deformed space with minimal length
• Deformed Heisenberg algebra and minimal length
• Quantization and Conformal Properties of a Generalized Calogero Model
• Gravitational Effects in Quantum Mechanics
• Experimental Search for Quantum Gravity
• Quantum cosmology, minimal length and holography
• Lagrangian Formulation of a Magnetostatic Field in the Presence of a Minimal Length Scale Based on the Kempf Algebra
• Generalized uncertainty principle in resonant detectors of gravitational waves
• Exactly solvable problems in the momentum space with a minimum uncertainty in position
• The Mixmaster Universe in a generalized uncertainty principle framework
• The quantum N-body problem with a minimal length
• Quantum-spacetime effects on nonrelativistic Schrödinger evolution
• Matrix oscillator and Calogero-type models
• Dirac $\delta$-function potential in quasiposition representation of a minimal-length scenario
• Massive fermions interacting via a harmonic oscillator in the presence of a minimal length uncertainty relation
• Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty
• Noncommutative spaces and covariant formulation of statistical mechanics
• Quantum gravitational decoherence of a mechanical oscillator from spacetime fluctuations
• Relation of deformed nonlinear algebras with linear ones
• Resonant detectors of gravitational wave in the linear and quadratic generalized uncertainty principle framework
• Solutions of the Bogoliubov-de Gennes equation with position dependent Fermi--velocity and gap profiles
• The generalized uncertainty principle in the presence of extra dimensions
• Exact solutions for two-body problems in 1D deformed space with minimal length
• Inequivalent quantization of the rational Calogero model with a Coulomb type interaction
• Large Extra Dimensions and the Minimal Length
• Bound states in the continuum are universal under the effect of minimal length
• A note on scattering in deformed space with minimal length
• Exact continuity equation in a space with minimal length