A Vlasov-Schrödinger-Poisson system is studied, modeling the transport and interactions of electrons in a bidimensional electron gas. The particles are assumed to have a wave behaviour in the confinement direction (z ) and to behave like point particles in the directions parallel to the electron gas (x). For each fixed x and at each time t, the eigenfunctions and the eigen-energies of the Schrödinger operator in the z are computed. The occupation number of each eigenfunction is computed through the resolution of a Vlasov equation in the x direction, the force field being the gradient of the eigen-energy. The whole system is coupled to the Poisson equation for the electrostatic interaction. Existence of weak solutions is shown for boundary value problems in the stationary and time-dependent regimes.