  A general program to show quantum-classical correspondence for bound
conservative integrable and chaotic systems is described. The method is applied
to integrable systems and the nature of the approach to the classical limit,
the cancellation of essential singularities, is demonstrated. The application
to chaotic systems requires an understanding of classical Liouville
eigenfunctions and a Liouville spectral decomposition, developed herein.
General approaches to the construction of these Liouville eigenfunctions and
classical spectral projectors in quantum and classical mechanics are discussed
and are employed to construct Liouville eigenfunctions for classically chaotic
systems. Correspondence for systems whose classical analogs are chaotic is
discussed, based on this decomposition, in the following paper.
