  We consider the energy spectrum of the planar quantum well which consisted of
two ribbons of narrow-gap semiconductors and a graphene ribbon between ones. It
is shown that the gapless mode appears only in case of inverted narrow-gap
semiconductors. Spin splitting of the energy spectrum for a nonsymmetric
quantum well is calculated taking into account a specificity of graphene. We
investigate interface states and optical transitions. It is shown that the
optical transitions are possible only with a conservation of a parity.
