Dirac equation in (1 + 1) dimensional curved space-time: Bound states and bound states in continuum

We study Dirac equation in (1 + 1) dimensional curved space-time. In particular, it is shown that bound states can be found in the presence of interactions in certain curved spaces. It has also been shown that solutions of the free particle Dirac equation when mapped to some suitable curved spaces become bound states in continuum. A number of examples have been considered and complete solutions have been obtained analytically in each case. (paper)