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.
Categories: math-ph math.MP