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In this paper a theoretical studies of the space separation of electron andhole wave functions in the quantum well ZnO/Mg0.27Zn0.73O are presented. Forthis aim the self-consistent solution of the Schr\"odinger equations forelectrons and holes and the Poisson equations at the presence of spatiallyvarying quantum well potential due to the piezoelectric effect and localexchange-correlation potential is found. The one-dimensional Poisson equationcontains the Hartree potential which includes the one-dimensional chargedensity for electrons and holes along the polarization field distribution. Thethree-dimensional Poisson equation contains besides the one-dimensional chargedensity for electrons and holes the exchange-correlation potential which isbuilt on convolutions of a plane-wave part of wave functions in addition. InZnO/(Zn,Mg)O quantum well the electron-hole pairing leads to the excitoninsulator 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 thanif they are paired. The particle-hole pairing leads to the Cooper instability.

Exciton insulator states for particle-hole pair in ZnO/(Zn,Mg)O quantum wells and for Dirac cone