Relativistic wave equations are solved exactly in the classical space-time background of a two-dimensional gravitational theory. In the simplest nontrivial geometry without horizons, the solutions are necessarily bound states and the constraints on the energy eigenvalues are determined. Aspects of quantum field theory in the background of the (1+1)-dimensional black hole are also examined.

• Received 22 October 1990

DOI:https://doi.org/10.1103/PhysRevD.43.3948