Levinson's theorem and reflectionless one-dimensional potentials

Details Levinson's theorem and reflectionless one-dimensional potentials Levinson's theorem and reflectionless one-dimensional potentials

2005-10-04

arxiv.org/abs/quant-ph/0510026v2

Physics

Quantum Physics

7 pages, no figures

Scientific paper

We studied two possible approaches to one-dimensional Levinson's theorem for Sch\"odinger equation. The first one, we restrict the 3-dimensional theorem. The other one, the theorem proposed by Dong, Ma and Klauss \cite{Dong}. We find failures in each approach for a one-dimensional reflectionless potential. In order to see this, we explicitly evaluate the phase shift using Schr\"odinger equation using solution procedure proposed by Jaffe \cite{Jaffe}.

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