(a) Institute for Nuclear Problems, Belarus State University, Bobruiskaya 11,220050 Minsk, Belarus(b) Institut fu¨r Festko¨rperphysik, Technische Universita¨t Berlin, Hardenbergstr. 36,10623 Berlin, Germany(Received September 4, 2001; in revised form October 5, 2001; accepted October 17, 2001)Subject classification: 42.25.–p; 78.66.Sq; 85.35.BeA self-consistent microscopic local-field theory for an isolated arbitrary shaped quantum dot(QD) has been presented. In our approach we introduce into the Schro¨dinger equation a depo-larization field induced by an external electromagnetic field, and combine this idea with thesecond quantization technique for electron–hole pairs. As a result, we succeeded in deriving thegeneral self-consistent nonlinear equations for the system “QD + classical electromagnetic field”.In the linear approximation, our approach reproduces microscopically the depolarization shift ofthe QD gain band and, in anisotropically shaped QDs, polarization dependent splitting of thisband.
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