  Anisotropic Kepler problem is investigated by perturbation method in both
classical and quantum mechanics. In classical mechanics, due to the singularity
of the potential, global diffusion in phase space occurs at an arbitrarily
small perturbation parameter. In quantum mechanics, the singularity induces a
large transition amplitude between quasi degenerate eigen states, which
generically decays as $\hbar$ in the semi-classical limit.
