Harmonic oscillator with minimal length uncertainty relations and ladder operators
Ivan Dadic, Larisa Jonke, Stjepan Meljanac
TL;DR
This paper develops ladder operators for harmonic oscillators under minimal length uncertainty, explores their algebraic structure, and examines the symmetry properties of these noncommutative systems.
Contribution
It introduces a method to construct creation and annihilation operators for deformed harmonic oscillators with minimal length uncertainty relations.
Findings
Ladder operators are explicitly constructed for the deformed harmonic oscillator.
The paper discusses the dynamical symmetry of noncommutative harmonic oscillators.
A potential generalization to other deformations of canonical commutation relations is proposed.
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.
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