Levinson’s theorem, zero‐energy resonances, and time delay in one‐dimensional scattering systems

The one‐dimensional Levinson’s theorem is derived and used to study zero‐energy resonances in a double‐potential system. The low energy behavior of time delay is also investigated. In particular, it is shown that the quantum mechanical time delay admits a classical lower bound, in the low energy limit, if the potential has no bound‐state solutions.