The Noncommutative Quadratic Stark Effect For The H-Atom
  Using both the second order correction of perturbation theory and the exact computation due to Dalgarno-Lewis, we compute the second order noncommutative Stark effect,i.e., shifts in the ground state energy of the hydrogen atom in the noncommutative space in an external electric field. As a side result we also obtain a sum rule for the mean oscillator strength. The energy shift at the lowest order is quadratic in both the electric field and the noncommutative parameter $\theta$. As a result of noncommutative effects the total polarizability of the ground state is no longer diagonal. 
Noureddine Chair, Mohammad A. Dalabeeh