dorsal/arxiv
View SchemaScattering by a contact potential in three and lower dimensions
| Authors | Qiong-gui Lin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0103013 |
| URL | https://arxiv.org/abs/quant-ph/0103013 |
| DOI | 10.1088/0305-4470/34/9/308 |
| Journal | J. Phys. A 34 (2001) 1911-1918 |
Abstract
We consider the scattering of nonrelativistic particles in three dimensions by a contact potential $\Omega\hbar^2\delta(r)/ 2\mu r^\alpha$ which is defined as the $a\to 0$ limit of $\Omega\hbar^2\delta(r-a)/2\mu r^\alpha$. It is surprising that it gives a nonvanishing cross section when $\alpha=1$ and $\Omega=-1$. When the contact potential is approached by a spherical square well potential instead of the above spherical shell one, one obtains basically the same result except that the parameter $\Omega$ that gives a nonvanishing cross section is different. Similar problems in two and one dimensions are studied and results of the same nature are obtained.
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"abstract": "We consider the scattering of nonrelativistic particles in three dimensions\nby a contact potential $\\Omega\\hbar^2\\delta(r)/ 2\\mu r^\\alpha$ which is defined\nas the $a\\to 0$ limit of $\\Omega\\hbar^2\\delta(r-a)/2\\mu r^\\alpha$. It is\nsurprising that it gives a nonvanishing cross section when $\\alpha=1$ and\n$\\Omega=-1$. When the contact potential is approached by a spherical square\nwell potential instead of the above spherical shell one, one obtains basically\nthe same result except that the parameter $\\Omega$ that gives a nonvanishing\ncross section is different. Similar problems in two and one dimensions are\nstudied and results of the same nature are obtained.",
"arxiv_id": "quant-ph/0103013",
"authors": [
"Qiong-gui Lin"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/34/9/308",
"journal_ref": "J. Phys. A 34 (2001) 1911-1918",
"title": "Scattering by a contact potential in three and lower dimensions",
"url": "https://arxiv.org/abs/quant-ph/0103013"
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