dorsal/arxiv
View SchemaLevinson's theorem and reflectionless one-dimensional potentials
| Authors | D. E. Zambrano |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0510026 |
| URL | https://arxiv.org/abs/quant-ph/0510026 |
Abstract
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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"date_created": "2026-03-02T18:02:19.684000Z",
"date_modified": "2026-03-02T18:02:19.684000Z",
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"abstract": "We studied two possible approaches to one-dimensional Levinson\u0027s theorem for\nSch\\\"odinger equation. The first one, we restrict the 3-dimensional theorem.\nThe other one, the theorem proposed by Dong, Ma and Klauss \\cite{Dong}. We find\nfailures in each approach for a one-dimensional reflectionless potential. In\norder to see this, we explicitly evaluate the phase shift using Schr\\\"odinger\nequation using solution procedure proposed by Jaffe \\cite{Jaffe}.",
"arxiv_id": "quant-ph/0510026",
"authors": [
"D. E. Zambrano"
],
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"quant-ph"
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"title": "Levinson\u0027s theorem and reflectionless one-dimensional potentials",
"url": "https://arxiv.org/abs/quant-ph/0510026"
},
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