EXACT BOGOMOLNY SECTIONS FOR SEPARABLE SYSTEMS

A good Poincare section of a classical dynamical system defines a mapp ing that provides essential qualitative information about its orbits. Bogomolny's sections in quantum mechanics lead to an eigenvalue condit ion that depends on the Poincare map in the semi-classical limit. The conditions for the construction of purely quantum mechanical Bogomolny -Green functions are discussed here with reference to separable system s. For appropriately chosen Green functions the ensuing eigenvalue con dition is shown to be exact. This result is valid even if not a single classical orbit crosses the surface of section.