The WKB approximation for the nonlinear Schrodinger-Poisson system (NSP) is considered. The system can be transformed into the compressible Euler-Poisson system with a so-called dispersive term by the well known Madlung transform. It is then expected that the solution to NSP system is approximating the solution to the compressible Euler-Poisson system. We show this holds for two dimensional case by applying the sharp order
estimate of the Gagliardo-Nirenberg inequality.

This is a joint work with S. Masaki (Hiroshima University).