  A topological superconductor is a fully gapped superconductor that exhibits
exotic zero-energy Andreev surface states at interfaces with a normal metal. In
this paper we investigate the properties of a three-dimensional time reversal
invariant topological superconductor by means of a two-band model with
unconventional pairing in both the inter- and intraband channels. Due to the
bulk-boundary correspondence the presence of Andreev surface states in this
system is directly related to the topological structure of the bulk
wavefunctions, which is characterized by a winding number. Using quasiclassical
scattering theory we construct the spectrum of the Andreev bound states that
appear near the surface and compute the surface density of states for various
surface orientations. Furthermore, we consider the effects of band splitting,
i.e., the breaking of an inversion-type symmetry, and demonstrate that in the
absence of band splitting there is a direct transition between the fully gapped
topologically trivial phase and the nontrivial phase, whereas in the presence
of band splitting there exists a finite region of a gapless nodal
superconducting phase between the fully gapped topologically trivial and
nontrivial phases.
