  We first compare the mathematical structure of quantum and classical
mechanics when both are formulated in a C*-algebraic framework. By using finite
von Neumann algebras, a quantum mechanical analogue of Liouville's theorem is
then proposed. We proceed to study Poincare recurrence in C*-algebras by
mimicking the measure theoretic setting. The results are interpreted as
recurrence in quantum mechanics, similar to Poincare recurrence in classical
mechanics.
