%0 Journal Article
%T Position-dependent noncommutative quantum models: Exact solution of the harmonic oscillator
%A Dine Ousmane Samary
%J Mathematics
%D 2013
%I arXiv
%X This paper is devoted to find the exact solution of the harmonic oscillator in a position-dependent 4-dimensional noncommutative phase space. The noncommutative phase space that we consider is described by the commutation relations between coordinates and momenta: $[\hat{x}^1,\hat{x}^2]=i\theta(1+\omega_2 \hat x^2)$, $[\hat{p}^1,\hat{p}^2]=i\bar\theta$, $[\hat{x}^i,\hat{p}^j]=i\hbar_{eff}\delta^{ij}$. We give an analytical method to solve the eigenvalue problem of the harmonic oscillator within this deformation algebra.
%U http://arxiv.org/abs/1307.7628v4