dorsal/arxiv
View SchemaScattering in one dimension: The coupled Schroedinger equation, threshold behaviour and Levinson's theorem
| Authors | K. A. Kiers, W. van Dijk |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9608032 |
| URL | https://arxiv.org/abs/quant-ph/9608032 |
| DOI | 10.1063/1.531762 |
| Journal | J.Math.Phys.37:6033-6059,1996 |
Abstract
We formulate scattering in one dimension due to the coupled Schr\"{o}dinger equation in terms of the $S$ matrix, the unitarity of which leads to constraints on the scattering amplitudes. Levinson's theorem is seen to have the form $\eta(0) = \pi (n_b + 1/2 n - 1/2 N)$, where $\eta(0)$ is the phase of the $S$ matrix at zero energy, $n_b$ the number of bound states with nonzero binding energy, $n$ the number of half-bound states, and $N$ the number of coupled equations. In view of the effects due to the half-bound states, the threshold behaviour of the scattering amplitudes is investigated in general, and is also illustrated by means of particular potential models.
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"abstract": "We formulate scattering in one dimension due to the coupled Schr\\\"{o}dinger\nequation in terms of the $S$ matrix, the unitarity of which leads to\nconstraints on the scattering amplitudes. Levinson\u0027s theorem is seen to have\nthe form $\\eta(0) = \\pi (n_b + 1/2 n - 1/2 N)$, where $\\eta(0)$ is the phase of\nthe $S$ matrix at zero energy, $n_b$ the number of bound states with nonzero\nbinding energy, $n$ the number of half-bound states, and $N$ the number of\ncoupled equations. In view of the effects due to the half-bound states, the\nthreshold behaviour of the scattering amplitudes is investigated in general,\nand is also illustrated by means of particular potential models.",
"arxiv_id": "quant-ph/9608032",
"authors": [
"K. A. Kiers",
"W. van Dijk"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.531762",
"journal_ref": "J.Math.Phys.37:6033-6059,1996",
"title": "Scattering in one dimension: The coupled Schroedinger equation, threshold behaviour and Levinson\u0027s theorem",
"url": "https://arxiv.org/abs/quant-ph/9608032"
},
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