Levinson’s theorem, zero-energy resonances, and time delay in one- dimensional scattering systems. (English) Zbl 0807.35120
Summary: 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.
MSC:
| 35Q40 | PDEs in connection with quantum mechanics |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81U05 | \(2\)-body potential quantum scattering theory |
References:
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