  In this paper, we study the quasineutral limit and asymptotic behaviors for
the quantum Navier-Stokes-Possion equation. We apply a formal expansion
according to Debye length and derive the neutral incompressible Navier-Stokes
equation. To establish this limit mathematically rigorously, we derive uniform
(in Debye length) estimates for the remainders, for well-prepared initial data.
It is demonstrated that the quantum effect do play important roles in the
estimates and the norm introduced depends on the Planck constant $\hbar>0$.
