Harmonic oscillator with minimal length uncertainty relations and ladder operators

2002/10/31 by I. Dadić, Ivan Dadic, Larisa Jonke +1 · 83 citations
Mathematics · Physics and Astronomy · #Anharmonicity #Annihilation #Class (philosophy) #Coherent states #Commutation #Computer science #Construct (python library) #Creation and annihilation operators #Generalization #Geometry #Harmonic #Harmonic oscillator #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Symmetry (geometry) #hep-th

paper · pdf · doi:10.1103/physrevd.67.087701

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 67(8) (American Physical Society) · 8 pages, revtex4, final version, to appear in PRD

arxiv created 2003/01/20 · openalex publication_date 2003/04/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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

Citations

• Realization of the annihilation operator for generalized oscillator-like system by a differential operator
• The Generalized Uncertainty Principle and Black Hole Remnants
• Exchange operator formalism for integrable systems of particles
• Representations of non-commutative quantum mechanics and symmetries
• String theory beyond the Planck scale
• Exact solution of the harmonic oscillator in arbitrary dimensions with minimal length uncertainty relations
• Doubly-Special Relativity: First Results and Key Open Problems
• Minimal length uncertainty relation and the hydrogen atom
• Trans-Planckian effects in inflationary cosmology and the modified uncertainty principle

Cited by

• Quantization and conformal properties of a generalized Calogero model