dorsal/arxiv
View SchemaOrthogonal polynomial solutions to the non-central modified Kratzer potential
| Authors | F. Yasuk, I. Boztosun, A. Durmus |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0605007 |
| URL | https://arxiv.org/abs/quant-ph/0605007 |
Abstract
We investigate the analytical solution of a new exactly solvable non-central potential of $V(r,\theta) = D({\frac{r - a}{r}})^2+{\frac{\beta}{r^2\sin^2 \theta}}+{\frac{\gamma \cos \theta}{r^2\sin^2 \theta}}$ type, which may be called as the modified non-central Kratzer potential. The energy eigenvalues as well as the corresponding eigenfunctions are calculated for various values of $n$ and $m$ quantum numbers within the framework of the Nikiforov-Uvarov and Asymtotic Iteration Methods for the $CO$ diatomic molecule as an application of this potential. In this paper, we first present the effect of the non-central term on the bound-state energy eigenvalues: this effect is determined explicitly for different $n$ and $m$ quantum numbers with $\beta=\gamma$=0.0, 0.1, 1.0 and 5.0 values and the results are compared with the findings of the modified Kratzer potential for different $n$ and $l$ quantum numbers. Then, we show that the angle-dependent non-central part behaves like a centrifugal barrier and it reduces the depth of the attractive potential pocket, which effects the bound-state energy eigenvalues.
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"abstract": "We investigate the analytical solution of a new exactly solvable non-central\npotential of $V(r,\\theta) = D({\\frac{r - a}{r}})^2+{\\frac{\\beta}{r^2\\sin^2\n\\theta}}+{\\frac{\\gamma \\cos \\theta}{r^2\\sin^2 \\theta}}$ type, which may be\ncalled as the modified non-central Kratzer potential. The energy eigenvalues as\nwell as the corresponding eigenfunctions are calculated for various values of\n$n$ and $m$ quantum numbers within the framework of the Nikiforov-Uvarov and\nAsymtotic Iteration Methods for the $CO$ diatomic molecule as an application of\nthis potential. In this paper, we first present the effect of the non-central\nterm on the bound-state energy eigenvalues: this effect is determined\nexplicitly for different $n$ and $m$ quantum numbers with $\\beta=\\gamma$=0.0,\n0.1, 1.0 and 5.0 values and the results are compared with the findings of the\nmodified Kratzer potential for different $n$ and $l$ quantum numbers. Then, we\nshow that the angle-dependent non-central part behaves like a centrifugal\nbarrier and it reduces the depth of the attractive potential pocket, which\neffects the bound-state energy eigenvalues.",
"arxiv_id": "quant-ph/0605007",
"authors": [
"F. Yasuk",
"I. Boztosun",
"A. Durmus"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP"
],
"title": "Orthogonal polynomial solutions to the non-central modified Kratzer potential",
"url": "https://arxiv.org/abs/quant-ph/0605007"
},
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