Levinson's theorem and reflectionless one-dimensional potentials

D. E. Zambrano

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arXiv · quant-ph/0510026

Levinson's theorem and reflectionless one-dimensional potentials

D. E. Zambrano

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Abstract

We studied two possible approaches to one-dimensional Levinson's theorem for Schödinger 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 Schrödinger equation using solution procedure proposed by Jaffe \cite{Jaffe}.

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D. E. Zambrano. 2006-07-05. Levinson's theorem and reflectionless one-dimensional potentials. https://arxiv.org/abs/quant-ph/0510026

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