dorsal/arxiv
View SchemaA perturbative treatment for the bound states of the Hellmann potential
| Authors | Sameer M. Ikhdair, Ramazan Sever |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0603205 |
| URL | https://arxiv.org/abs/quant-ph/0603205 |
| Journal | THEOCHEM 809, 103 (2007) |
Abstract
A new approximation formalism is applied to study the bound states of the Hellmann potential, which represents the superposition of the attractive Coulomb potential $-a/r$ and the Yukawa potential $b\exp (-\delta r)/r$ of arbitrary strength $b$ and screening parameter $\delta $. Although the analytic expressions for the energy eigenvalues $E_{n,l\text{}}$ yield quite accurate results for a wide range of $n,\ell $ in the limit of very weak screening, the results become gradually worse as the strength $b$ and the screening coefficient $\delta $ increase. This is because that the expansion parameter is not sufficiently small enough to guarantee the convergence of the expansion series for the energy levels.
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"abstract": "A new approximation formalism is applied to study the bound states of the\nHellmann potential, which represents the superposition of the attractive\nCoulomb potential $-a/r$ and the Yukawa potential $b\\exp (-\\delta r)/r$ of\narbitrary strength $b$ and screening parameter $\\delta $. Although the analytic\nexpressions for the energy eigenvalues $E_{n,l\\text{}}$ yield quite accurate\nresults for a wide range of $n,\\ell $ in the limit of very weak screening, the\nresults become gradually worse as the strength $b$ and the screening\ncoefficient $\\delta $ increase. This is because that the expansion parameter is\nnot sufficiently small enough to guarantee the convergence of the expansion\nseries for the energy levels.",
"arxiv_id": "quant-ph/0603205",
"authors": [
"Sameer M. Ikhdair",
"Ramazan Sever"
],
"categories": [
"quant-ph"
],
"journal_ref": "THEOCHEM 809, 103 (2007)",
"title": "A perturbative treatment for the bound states of the Hellmann potential",
"url": "https://arxiv.org/abs/quant-ph/0603205"
},
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