On the derivation of a nonlinear schrödinger equation for impurity center electrons in ionic crystals

Abstract

For the calculation of electronic wave functions of semiconducting crystals Pekar [1] assumed a coupling between impurity center electrons and a polarizable continuum. Eliminating the equilibirum polarization by application of the energy minimum principle he obtained a nonlinear Schrodinger equation for the impurity center electrons alone. In this paper Pekar’s continuum theoretical method is substituted by atomistic description. In adiabatic approximation the energy of a crystal containing one F-center is evaluated by a Hartree-Fock procedure. Both polarization and displacement dipoles of the lattice ions are eliminated, and by variation with respect to the F-center wave function the atomistic analogon of Pekar’s equation is obtained.