  Nonlinear Schrodinger Equations (NLS) of the Hartree type occur in the
modeling of quantum semiconductor devices. Their "semiclassical" limit of
vanishing (scaled) Planck constant is both a mathematical challenge and
practically relevant when coupling quantum models to classical models.
  With the aim of describing the semi-classical limit of the 3D
Schrodinger--Poisson system with an additional harmonic potential, we study
some semi-classical limits of the Hartree equation with harmonic potential in
space dimension n>1. The harmonic potential is confining, and causes focusing
periodically in time. We prove asymptotics in several cases, showing different
possible nonlinear phenomena according to the interplay of the size of the
initial data and the power of the Hartree potential. In the case of the 3D
Schrodinger-Poisson system with harmonic potential, we can only give a formal
computation since the need of modified scattering operators for this long range
scattering case goes beyond current theory. We also deal with the case of an
additional "local" nonlinearity given by a power of the local density - a model
that is relevant when incorporating the Pauli principle in the simplest model
given by the "Schrodinger-Poisson-X$\alpha$ equation". Further we discuss the
connection of our WKB based analysis to the Wigner function approach to
semiclassical limits.
