Singularity in classical and quantum Kepler Problem with Weak Anisotropy
Zai-Qiao Bai, Wei-Mou Zheng
Abstract
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 in the semi-classical limit.
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