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| Format: | Preprint |
| Veröffentlicht: |
2017
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| Online-Zugang: | https://arxiv.org/abs/1711.10322 |
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| _version_ | 1866915968227213312 |
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| author | Badalov, V. H. Baris, B. Uzun, K. |
| author_facet | Badalov, V. H. Baris, B. Uzun, K. |
| contents | In this paper, the approximate analitical solutions of the hyper-radial Schrödinger equation are obtained for the generalized Wood-Saxon potential by implementing the Pekeris approximation to surmount the centrifugal term. The energy eigenvalues and corresponding hyper-radial wave functions are found for any angular momentum case via the Nikiforov-Uvarov (NU) and Supersymmetric quantum mechanics (SUSY QM) methods. Hence, the same expressions are obtained for the energy eigenvalues, and the expression of hyper-radial wave functions transformed each other is shown owing to these methods. Furthermore, a finite number energy spectrum depending on the depths of the potential well $V_{0}$ and $W$, the radial $n_{r}$ and $l$ orbital quantum numbers and parameters $D,a,R_{0}$ are also identified in detail. Finally, the bound state energies and the corresponding normalized hyper-radial wave functions for the neutron system of the a $^{56} Fe$ nucleus are calculated in $D=2$ and $D=3$, as well as the energy spectrum expressions of other highest dimensions are identified by using the energy spectrum of $D=2$ and $D=3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1711_10322 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Bound states of the $D$-dimensional Schrödinger equation for the generalized Woods-Saxon potential Badalov, V. H. Baris, B. Uzun, K. Nuclear Theory Mathematical Physics In this paper, the approximate analitical solutions of the hyper-radial Schrödinger equation are obtained for the generalized Wood-Saxon potential by implementing the Pekeris approximation to surmount the centrifugal term. The energy eigenvalues and corresponding hyper-radial wave functions are found for any angular momentum case via the Nikiforov-Uvarov (NU) and Supersymmetric quantum mechanics (SUSY QM) methods. Hence, the same expressions are obtained for the energy eigenvalues, and the expression of hyper-radial wave functions transformed each other is shown owing to these methods. Furthermore, a finite number energy spectrum depending on the depths of the potential well $V_{0}$ and $W$, the radial $n_{r}$ and $l$ orbital quantum numbers and parameters $D,a,R_{0}$ are also identified in detail. Finally, the bound state energies and the corresponding normalized hyper-radial wave functions for the neutron system of the a $^{56} Fe$ nucleus are calculated in $D=2$ and $D=3$, as well as the energy spectrum expressions of other highest dimensions are identified by using the energy spectrum of $D=2$ and $D=3$. |
| title | Bound states of the $D$-dimensional Schrödinger equation for the generalized Woods-Saxon potential |
| topic | Nuclear Theory Mathematical Physics |
| url | https://arxiv.org/abs/1711.10322 |