The exact solutions of Kane equations which have position-dependence band gap in an external non-uniform electric field

The energy spectrum of electrons in narrow band gap semiconductor nanocrystals which have position dependence band gap in an external non-uniform electric field which compensate the position dependence of the band edge of the valence band potential are studied theoretically taking into account the non-parabolicity of electrons in dispersion laws. The exact solutions of the Kane equations with strong spin-orbital interaction are determined with and without magnetic field via the band gap changes as a function of the position. The position dependence of the band gap is taken parabolically.