  Quasiparticle bound states are found theoretically on transparent interfaces
of d-wave superconductors (dSC) with charge density wave solids (CDW), as well
as s-wave superconductors (sSC) with d-density waves (DDW). These bound states
represent a combined effect of Andreev reflection from the superconducting side
and an unconventional quasiparticle Q-reflection from the density wave solid.
If the order parameter for a density wave state is much less than the Fermi
energy, bound states with almost zero energy take place for an arbitrary
orientation of symmetric interfaces. For larger values of the order parameter,
dispersionless zero-energy states are found only on (110) interfaces. Two
dispersive energy branches of subgap quasiparticle states are obtained for
(100) symmetric interfaces. Andreev low-energy bound states, taking place in
junctions with CDW or DDW interlayers, result in anomalous junction properties,
in particular, the low-temperature behavior of the Josephson critical current.
