An analytical expression for the Green function is derived for an independent electron which moves in a one-dimensional space with a double-square potential barrier. A perturbation theory is constructed for a system of interacting electrons and the effect of the Coulomb interaction on resonant tunneling phenomena is studied. Solving numerically the Dyson equation of the one-dimensional system in the Hartree approximation, the self-consistent Green function is computed, from which the trans-mission probability through the barrier and the density of states within the well region have been calculated and analyzed. The impurity Anderson model is examined in comparison with the present model of more fundamental nature. Our method is expected to be applied to studies of other types of interaction in an inhomogeneous system in quasi-one-dimension.
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