The band motion of muons in superconductors is studied in detail. Both the damping rate and the effective mass of the muon due to the interaction with conduction electrons are examined. Then, the average hopping rate of a muon is obtained by combining these quantities. The results are compared with that obtained by the double-well model and the relation between the two is discussed. In addition, as an extention of our theory, the quantum diffusion in some unconventional superconductors is also examined.
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