dorsal/arxiv
View SchemaExact Solutions of the two-dimensional Schr\"{o}dinger equation with certain central potentials
| Authors | Shi-Hai Dong |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0003100 |
| URL | https://arxiv.org/abs/quant-ph/0003100 |
Abstract
By applying an ansatz to the eigenfunction, an exact closed form solution of the Schr\"{o}dinger equation in 2D is obtained with the potentials, $V(r)=ar^2+br^4+cr^6$, $V(r)=ar+br^2+cr^{-1}$ and $V(r)=ar^2+br^{-2}+cr^{-4}+dr^{-6}$, respectively. The restrictions on the parameters of the given potential and the angular momentum $m$ are obtained.
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"abstract": "By applying an ansatz to the eigenfunction, an exact closed form solution of\nthe Schr\\\"{o}dinger equation in 2D is obtained with the potentials,\n$V(r)=ar^2+br^4+cr^6$, $V(r)=ar+br^2+cr^{-1}$ and\n$V(r)=ar^2+br^{-2}+cr^{-4}+dr^{-6}$, respectively. The restrictions on the\nparameters of the given potential and the angular momentum $m$ are obtained.",
"arxiv_id": "quant-ph/0003100",
"authors": [
"Shi-Hai Dong"
],
"categories": [
"quant-ph"
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"title": "Exact Solutions of the two-dimensional Schr\\\"{o}dinger equation with certain central potentials",
"url": "https://arxiv.org/abs/quant-ph/0003100"
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