  Harmonic oscillator in noncommutative two dimensional lattice are
investigated. Using the properties of non-differential calculus and its
applications to quantum mechanics, we provide the eigenvalues and
eigenfunctions of the corresponding Hamiltonian. First we consider the case of
ordinary quantum mechanics, and we point out the thermodynamic properties of
the model. Then we consider the same question when both coordinates and
momentums are noncommutative.
