## Position Depending Noncommutative Quantum Models: Exact solution of harmonic oscillator    [PDF]

Dine Ousmane Samary
This paper devoted to find the exact solution of the harmonic oscillator in position-depend 4-dimensions non-commutative phase space. The noncommutative space that we consider is described by the commutation relation between coordinates and momentums: $[\hat{x}^1,\hat{x}^2]=i\theta(1+\omega_2 \hat x^2)$, $[\hat{p}^1,\hat{p}^2]=i\bar\theta$, $[\hat{x}^i,\hat{p}^j]=i\hbar_{eff}\delta^{ij}$. We give an analytical method to solve the corresponding eigenvalues problem of harmonic oscillator with this deformation.
View original: http://arxiv.org/abs/1307.7628