  In this paper, we consider the long wavelength limit for the quantum
Euler-Poisson equation. Under the Gardner-Morikawa transform, we derive the
quantum Korteweg-de Vries (KdV) equation by a singular perturbation method. We
show that the KdV dynamics can be seen at time interval of order
$O(\epsilon^{-3/2})$. When the nondimensional quantum parameter $H=2$, it
reduces to the inviscid Burgers equation.
