  Using time-independent scattering matrices, we study how the effects of
nonclassical paths on the recurrence spectra of diamagnetic atoms can be
extracted from purely quantal calculations. This study reveals an intimate
relationship between two types of nonclassical paths: exotic ghost orbits and
diffractive orbits. This relationship proves to be a previously unrecognized
reason for the success of semiclassical theories, like closed-orbit theory, and
permits a comprehensive reformulation of the semiclassical theory that
elucidates its convergence properties.
