# Classical Oscillator Model on Canonical, Lie-Algebraic Deformation and Heisenberg-Weyl Algebra Deformation Nonrelativistic Space

Research paper by Cui-Bai Luo, Zheng-Wen Long, Chao-Yun Long, Shui-Jie Qin, Hai-Bo Luo

Indexed on: 12 Jan '13Published on: 12 Jan '13Published in: International Journal of Theoretical Physics

#### Abstract

The oscillator model on nonrelativistic Canonical (soft), Lie-Algebraic deformation noncommutative space and deformed Heisenberg-Weyl Algebra noncomutative phase space are analyzed. For canonical deformation the additional dynamical effects are absent. For two kinds of Lie-Algebraic deformation space the additional effects are generated. Remarkably angular frequency ωρ is stepfunction, non-periodic function, and contains imaginary frequency. The corresponding particle trajectory varies greatly along with the deformation and time parameter $$\hat{k}$$, t. For deformed Heisenberg-Weyl Algebra noncommutative phase space the additional corrections are generated. Kρ,ωρ and particle trajectory have constant second-order correction with deformation parameters Θ and Π, but the particle still keep trajectory of classical oscillator.