  In this paper a theoretical studies of the space separation of electron and
hole wave functions in the quantum well ZnO/Mg0.27Zn0.73O are presented. For
this aim the self-consistent solution of the Schr\"odinger equations for
electrons and holes and the Poisson equations at the presence of spatially
varying quantum well potential due to the piezoelectric effect and local
exchange-correlation potential is found. The one-dimensional Poisson equation
contains the Hartree potential which includes the one-dimensional charge
density for electrons and holes along the polarization field distribution. The
three-dimensional Poisson equation contains besides the one-dimensional charge
density for electrons and holes the exchange-correlation potential which is
built on convolutions of a plane-wave part of wave functions in addition. In
ZnO/(Zn,Mg)O quantum well the electron-hole pairing leads to the exciton
insulator states. An exciton insulator states with a gap 3.4 eV are predicted.
If the electron and hole are separated, their energy is higher on 0.2 meV than
if they are paired. The particle-hole pairing leads to the Cooper instability.
