LEVINSONS THEOREM, ZERO-ENERGY RESONANCES, AND TIME-DELAY IN ONE-DIMENSIONAL SCATTERING SYSTEMS

The one-dimensional Levinson's theorem is derived and used to study ze ro-energy resonances in a double-potential system. The low energy beha vior of time delay is also investigated. In particular, it is shown th at the quantum mechanical time delay admits a classical lower bound, i n the low energy limit, if the potential has no bound-state solutions.